The traditional proxy re-encryption (PRE) or conditional proxy re-encryption (CPRE) can re-encrypt infinite times on the delegator's cipher text. However many practical applications do not need this property, they prefer the delegator can control on the times the proxy can re-encrypt. In this paper, we introduce a new kind of proxy re-encryption: k-times proxy re-encryption (KPRE). To construct a concrete KPRE scheme, we add public/private key to the proxy. In k-times proxy re-encryption, the proxy can only re-encrypt k times, otherwise the proxy's private key will be exposed. We construct a concrete IND-RCCA secure KPRE scheme by combining the k-times signature and Libert et al's IND-RCCA PRE scheme in PKC'08.