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Generalized signcryption is a novel cryptographic primitive, which provides encryption and authenticity services simultaneously or separately. The known schemes have the low communication performance and fail to deliver data stream. Based on bilinear pairing, an efficient generalized signcryption scheme with the shortened ciphertext called BPGSC is proposed. Combined with the hash-chained mechanism and KEM/DEM (key encapsulation mechanism/data encapsulation mechanism), the hybrid BPGSC is proposed also. Formal security analysis showed that BPGSC is a provable secure scheme in random oracle model under GDH (Gap Diffie-Hellman) assumption. With present secure parameters, the data rate of proposed scheme is 76%. It has the highest communication performance in all of known schemes.