Because of this letter's references to severe persecution, this letter is dated to just prior to Peter's death during the period oif Nero's persecution of Christians in A.d. 64-65.

Sources:
Encountering the New Testament, Walter A. Elwell / Robert W. Yarbrough, 1998, Baker Books, page 362-363

A Survey of the New Testament, Third Edition, Robert H. Gundry, 1994, A Survey of the New Testament, Third Edition, Robert H. Gundry, 1994, Zondervan, page 437