The author of the book of Hebrews is not named in the epistle, so there is a mystery as to who actually wrote it. Hebrews was written to Jewish Christians somewhere around A.D. 67.
The earliest tradition from the late second century has Hebrews associated with the Apostle Paul. Many have pointed out that the style of Hebrews differs from Paul's other epistles. In Hebrews 2:3 the author says the message of salvation was attested to us by those who heard. This would seem to rule out Paul. The Muratorian fragment which may date back to the second century lists thirteen epistles written by the Apostle Paul and it does not include Hebrews among them.
Other possible candidates for authorship of Hebrews include: Luke, Barnabas, Apollos, and Clement of Rome. The Greek in Hebrews 11:32 suggests that the author was male. One plausible theory is that Luke wrote down the teaching of Paul. This could account for the early church tradition that associated Hebrews with the Apostle Paul. It also could explain the difference in style from the other Pauline epistles and the reference in Hebrews 2:3. If it was written by Luke this theory could explain why Hebrews was associated with Paul even if he was not the author. But as Origen said, only God knows who wrote Hebrews.