The Bible is quite silent on Peter's death as well as all the others, save for James.
The only mention of Peters death is:
21:18-19 Verily, verily, I say unto thee, When thou wast
young, thou girdedst thyself, and walkedst whither thou
wouldest: but when thou shalt be old, thou shalt stretch
forth thy hands, and another shall gird thee, and carry thee
whither thou wouldest not. 19 This spake he, signifying by
what death he should glorify God. And when he had spoken
this, he saith unto him, Follow me. (KJB)
Verse 19 seems to clearly indicate that Jesus is speaking of Peter's death. Tradition does hold that Peter was crucified in Rome, upside down, which could be described in the above passage, but this does seem like one of those questions we will not know this side of glory. The only thing we can tell, is that in his death, Peter would glorify God. Tradition does hold as well, that the upside down crucifixion was Peter's idea, that he was not worthy to be crucified as Jesus was.