This books is pseudoepigraphical, or not written by the person claiming to be the author. It is not Peter, whoever it was.
The Gospel of Peter, or Gospel according to Peter, is one of the non-Canonical gospels which were rejected as apocryphal by the Church Leaders and the Catholic Church's synods of Carthage and Rome, which established the New Testament canon. It was the first of the non-canonical gospels to be rediscovered, preserved in the dry sands of Egypt.
The Gospel of Peter was recovered in 1886, by the French archaeologist, Urbain Bouriant, in the modern Egyptian city of Akhmim (sixty miles north of Nag Hammadi). The 8th- or 9th-century manuscript had been respectfully buried with an Egyptian monk. The fragmentary Gospel of Peter was the first non-canonical gospel to have been rediscovered, preserved in the dry sand of Egypt. Publication, delayed by Bouriant until 1892, occasioned intense interest. From the passion sequence that is preserved, it is clear that the gospel was a narrative gospel, but whether a complete narrative similar to the canonical gospels or simply a Passion cannot be said.
Two other papyrus fragments from Oxyrhyncus (P.Oxy 4009 and P.Oxy. 2949) were uncovered later and published in 1972. They are possibly, but not conclusively, from the Gospel of Peter and would suggest, if they belonged, that the text was more than just a passion narrative. These small fragments both seem to give first person accounts of discussions between Jesus and Peter in situations prior to the Passion week.
A major focus of the surviving fragment of the Gospel of Peter is the passion narrative, which is notable for ascribing responsibility for the crucifixion of Jesus to Herod Antipas rather than to Pontius Pilate.
The Gospel of Peter explicitly claims to be the work of the Apostle Peter:
"And I with my companions was grieved; and being wounded in mind we hid ourselves:" — GoP, 7. "But I Simon Peter and Andrew my brother took our nets and went to the sea;" — GoP, 14.
The true author of the gospel remains a mystery. Although there are parallels with the three Synoptic Gospels, Peter does not use any of the material unique to Matthew or unique to Luke. Raymond E. Brown and others find that the author may have been acquainted with the synoptic gospels and even with the Gospel of John; Brown (The Death of the Messiah) even suggests that the author's source in the canonical gospels was transmitted orally, through readings in the churches, i.e. that the text is based on what the author remembers about the other gospels, together with his own embellishments.
Ron Cameron and others have further speculated the Gospel of Peter was written independently of the synoptic gospels using an early proto-gospel. A consequence of this is the potential existence of a source text that formed the basis of the passion narratives in Matthew, Luke, and Mark, as well as in Peter. Origen makes mention of the Gospel of Peter as agreeing with the tradition of the Hebrews. The relationship to the Gospel according to the Hebrews becomes more clear when Theodoret states that the Nazarenes made use of the Gospel of Peter, for we know by the testimony of the Fathers generally that the Nazarene Gospel was that commonly called the Gospel according to the Hebrews. The same Gospel was in use among the Ebionites, and in fact, as almost all critics are agreed, the Gospel according to the Hebrews, under various names, such as the Gospel according to Peter, according to the Apostles, the Nazarenes, Ebionites, Egyptians, &c, with modifications certainly, but substantially the same work, was circulated very widely throughout the early Church.
This book was probably not written by Peter. The visions are unlike the other gospels and the details seem skewed. Finally Peter describes himself hiding with the twelve apostles, even though there were only 11 at that point, since Judas killed himself.