Proxy signature, which allows an original signer to delegate his/her signing right to another party (or proxy signer), is very useful in many applications. Conventional proxy signature only allows the original signer to specify in the warrant the validity time period of the delegation but not the number of proxy signatures the proxy signer can generate. To address this problem, in this paper, we provide a formal treatment for k-time proxy signature. Such a scheme allows a designated proxy signer to produce only a fixed number of proxy signatures on behalf of the original signer. We provide the formal definitions and adversary models for k-time proxy signature, and propose an efficient construction which is provably secure against different types of adversaries.