In a proxy multi-signature scheme, a designated proxy signer can generate the signature on behalf of a group of original signers. Although some work has been done in proxy-multi signature schemes, until now there is no formalized definition and security model for them. In this paper, we will give the formal definition and a security model of proxy-multi signature scheme. We also constructed a proxy-multi signature scheme based on the BLS short signature scheme and proved its security in our security model.