I agree with BTS. It is an anonymous homily and its language, style, and theology distinguishes the author as a mind quite different from Paul. Because of the connections between Hebrews and Alexandrian typology and the Wisdom of Solomon (which was written in Alexandria), the book probably was written by an Alexandrian Christian as conjectured by Luther and later writers (who often suspected that Apollos was the author, although there is nothing that substantiates such an ascription).
One may note that the author does not construe himself as an apostle who received revelation directly from Christ: "This promise was first announced by the Lord himself, and is guaranteed to us by those who heard him" (Hebrews 2:3). Paul regularly emphasized his own apostolic status and his direct link to Jesus via personal revelation (Galatians 1:1-12, Romans 1:1, 1 Corinthians 15:8). The author of Hebrews instead aligns himself with his readers who have not had any direct connection with Jesus, but whose reception of the promise has been mediated by apostolic witnesses. The writer also does not use distinctive Paulinisms (like "Christ Jesus") and has a rather smooth rhetorical style that Origen (in Eusebius, Ecclesiastical History 6.25) noticed was very different from Paul's more rugged form of expression. The author's concept of the Law, faith, and especially the concept of Jesus as a high priest have no direct parallel in Paul. For instance, Jesus' death is viewed as facilitating "sanctification" rather than "justification" (Hebrews 2:11, 9:13, 10:14), which is quite conspicuous in light of Pauline theology but which conforms to Hebrews' priestly perspective.
It is also worth noting that the book was not accepted as canonical in Rome for a long time on account of its non-Pauline authorship:
"Paul’s fourteen epistles are well known and undisputed. It is not indeed right to overlook the fact that some have rejected the Epistle to the Hebrews, saying that it is disputed by the church of Rome, on the ground that it was not written by Paul. But what has been said concerning this epistle by those who lived before our time I shall quote in the proper place" (Eusebius, Ecclesiastical History 3.3.5).
And indeed, even as early as the second century AD, the book is omitted in the Muratonian Canon which reflects the views of the church at Rome. According to the tradition reported by Stephen Gobar, Irenaeus and Hippolytus both did not believe that the epistle was written by Paul, and Tertullian (whose Carthaginian brand of Latin Christianity was strongly influenced by Rome) specifically believed that Hebrews was written by Barnabas (De Pudicitia, 20). What is interesting about this tradition is that the epistle that was specifically attributed to this individual, Barnabas, displays a similar Alexandrian style. Barnabas was also depicted in Acts as a Levite Jew (compare the priestly perspective of Hebrews), and while he was recognized as an apostle by the later Church, the author of Acts (in 4:36-37) suggests that he converted to Christianity shortly after Pentacost (and thus was not a hearer of Jesus). Even into the fifth century AD, Jerome wrote concerning Hebrews that the "custom of the Latins received it not among the canonical scriptures" (Ad Dardanum, 129.3).
But what is interesting about the Roman reception of Hebrews is that the earliest trace of the epistle is, in fact, in the writings of Clement of Rome who wrote at the end of the first century AD (cf. Hebrews 1:3-13 = 1 Clement 36:2-5; 2:17, 3:1 = 1 Clement 36:1; 3:2, 5 = 1 Clement 43:1; 3:7, 10:15 = 1 Clement 13:1, 16:2; 4:12 = 1 Clement 21:9; 4:15 = 1 Clement 36:1; 6:18 = 1 Clement 27:2; 11:37 = 1 Clement 17:1; 12:9 = 1 Clement 64:1, etc.). The long historical survey on faith in Hebrews 11 is even imitated in 1 Clement 9-12. This suggests that Rome was either the original destination or place of origin of the homily, and the church there may have had firsthand knowledge of its authorship. If Rome was the original destination of the letter, the Roman rejection of Hebrews as canonical scripture is possibly due to the Roman community knowing that Paul was not its author, having its own local tradition of Hebrews' authorship which took a long time for the dominant view to supplant. The letter itself has a connection with Rome in the reference to the "those from Italy" (hoi apo tés Italias) in Hebrews 13:24, which would suggest either a Roman provenance or a Roman destination. The latter interpretation is probable since the use of apo "from" may more naturally refer to those are from a particular place but not living there at the time, and because the former interpretation is more natural by using en instead of apo, i.e. "those in Italy". They are thus Italians in the company of the author who send their greetings to those at home. But the present ending (13:18, 22-25) may not be original to the book, as it appears to dress up a lengthy homily as a (short!) quasi-Pauline epistle, with its mentions of imprisonment and Timothy (but no tradition of an imprisonment of Timothy exists either in Acts or in early tradition).