Multi-proxy signature (MPS) allows an original signer to authorize a group of proxy signers as his proxy agent to sign co-operatively a message. As per the literature, the relative computation cost of a pairing is approximately more than ten times of the scalar multiplication over elliptic curve group which indicates that pairing is a very expensive operation. Moreover the map-to-point function is also very expensive. Therefore, we propose a new MPS scheme without pairings having general crypto-graphic hash function after formalizing a security model.Our proposal is provable secure and much efficient than previously proposed schemes in practice.