In the past, proxy signature schemes were usually proposed to deal with one or two separate proxy conditions each. To make a difference, in this paper, the authors shall present a generalized version of proxy signature scheme. Compared to earlier proxy signature schemes, our novel scheme can be applied to every possible proxy situation. The proposed scheme allows the original group of original signers to delegate their signing capability to a designated proxy group. The proxy group of proxy signers can cooperatively generate a proxy signature on behalf of the original group. Any verifier can verify the proxy signature on the message with the knowledge of the identities of the actual original signers and the actual proxy signers. With this article, we also aim to demonstrate how to specify proxy signature schemes on elliptic curve over finite fields. In addition, some possible attacks have also been considered, and our security analysis will show that none of them can successfully break the proposed scheme.