A generalized group-oriented cryptosystem (GGOC) based on ElGamal cryptosystem was proposed by Yang et al. in 2003. This study shows that if the authorized decryption sets of users are not properly predetermined in Yang et al.’s GGOC, an unauthorized decryption set of users can recover the encrypted message without difficulty. This study also presents an improved protocol to resist such an attack. Key words: generalized group-oriented cryptosystem, access structure, security.