Who wrote the book of Hebrews?

That is an easy question. The answer is that no one knows who
wrote this book. It is one of my three or four personal favorite books in
the Bible, but, bottom line, the book is not signed. We can assume that
the very early church considered it to have “apostolic” authority, as it
was included in the very early list of inspired books, also known as the
“canon” of the New Testament.

Many have speculated about the author of Hebrews. Probably
the most common person to be attributed as author is the apostle Paul. It
is impossible to disprove this claim, but at least at first glance, the
style of writing seems to be dramatically different from anything we have
from Paul. Others have mentioned Timothy. Some have even speculated
that a female disciple wrote the book. We can probably assume that it was
written before AD 70 because of what is written in Hebrews 8:13. This
passage seems to imply that the destruction of Jerusalem (by the Roman
general Titus in AD 70) has not happened yet when the book was written.

I suggest you find a good commentary on the book of Hebrews.
In the introductory portion (assuming it is a good commentary) you will
find a section discussing most of the major theories on the authorship of
the book. In the end, if you are honest, you will perhaps have your
favorite theory, but you will say with the scholars that you do not know
who wrote this great book.

John Oakes