A proxy re-encryption (PRE) scheme allows a proxy to re-encrypt a ciphertext for Alice (delegator) to a ciphertext for Bob (delegatee) without seeing the underlying plaintext. However, existing PRE schemes generally suffer from at least one of the followings. Some schemes fail to provide the non-transferable property in which the proxy and the delegatee can collude to further delegate the decryption right to anyone. This is the main open problem left for PRE schemes. Other schemes assume the existence of a fully trusted private key generator (PKG) to generate the re-encryption key to be used by the proxy for re-encrypting a given ciphertext for a target delegatee. But this poses two problems in PRE schemes if the PKG is malicious: the PKG in their schemes may decrypt both original ciphertexts and re-encrypted ciphertexts (referred as the key escrow problem); and the PKG can generate reencryption key for arbitrary delegatees without permission from the delegator (we refer to it as the PKG despotism problem). In this paper, we propose the first non-transferable proxy re-encryption scheme which successfully achieves the nontransferable property. We show that the new scheme solved the PKG despotism problem and key escrow problem as well.