The concept of proxy re-cryptography comes from the work of Blaze, Bleumer, and Strauss in 1998. The goal of proxy re-encryption is to securely enable the re-encryption of ciphertexts from one key to another, without relying on trusted parties. In 2007, Matsuo proposed the concept of four types of proxy re-encryption schemes: CBE to CBE, IBE to CBE, CBE to IBE and IBE to IBE. Now CBE to IBE and IBE to IBE proxy re-encryption schemes are being standardized by IEEEP1363.3 working group. One feature of their schemes is that they are all based on BB1 identity based encryption. We reconsider the problem of constructing proxy re-encryption based on SK identity based encryption. Surprisingly, if we consider the help of PKG, then it is easy to construct proxy re-encryption based on SK identity based encryption. Interestingly , our proxy re-encryption scheme even can achieve CCA2 secure, which makes it is unique.