In this paper, a new efficient public key multi-messages multi-recipients elliptic curve signcryption (PK-MM-MR-ECS) scheme for provable secure communications has been proposed. The main idea of the proposed PK-MM-MR-ECS scheme is to design multi-key generator to generate multi-secret keys used to encrypt the multiple message for each recipient. The MKG played an important role for the communication overhead and computational cost saving in the proposed PK-MM-MR-ECS scheme. The numerical values for saving in communication overhead using the proposed scheme are 38.24% for two messages, two recipients and 67.97% for three messages, three recipients than does Zheng elliptic curve signcryption scheme with the same parameters. The proposed scheme costs 50% and 75% less in computation cost for two and four signcrypted messages over Zheng elliptic curve signcryption scheme respectively.