It is not known who wrote Hebrews. The ancient church was divided on this point until the late fourth century. At that time it was received as from Paul, mainly to justify its place in the canon. Martin Luther was the first to suggest Apollos as author on the grounds that he was from Alexandria. The epistle exhibits certain characteristics in vocabulary and thought matter typical of Alexandrian literary production. Curiously, the Alexandrian church never claimed the letter as its own.
Although Wesley accepted the traditional ascription of the letter to Paul, few would be prepared to do so today. The author was a second-generation Christian, having first heard the Gospel from one or more of the apostolic witnesses (2:3). A native Greek speaker, he was well educated and at points reflected thought modes of Alexandrian philosophy (see Williamson, “Platonism and Hebrews,” 423). On the other hand, he reflects a thoroughly Jewish frame of mind steeped in the LXX. He subscribed to current eschatological expectation and shared much of the theological perspective of Stephen and the Hellenists in Acts 6-8 (Manson, 167-71).
This, of course, is not so descriptive of Paul as someone else in the early apostolic circle. The style and vocabulary of the Greek in this epistle shows more classical refinement than any of Paul's letters. Was the author Apollos? Perhaps. But in Rome where the epistle early circulated, Tertullian (ca. a.d. 160-240) regarded Barnabas as the author. Acts 4:36 calls Barnabas a “Son of Encouragement,” well suiting him for this self-described “word of exhortation” (13:22). He was a Levite well acquainted with temple ritual and the Bible, a Greek Cypriot by birth, and an estate owner of means. Likely, he would have been educated and versed in Alexandrian thought. Other names have also been suggested, but no definitive pronouncement can be made as to who wrote Hebrews.