ElGamal public key encryption scheme has been designed in the 80's. It is one of the first partial homomorphic encryption and one of the first IND-CPA probabilistic public key encryption scheme. A linear version has been recently proposed by Boneh et al. In this paper, we present a linear encryption based on a generalized version of ElGamal encryption scheme. We prove that our scheme is IND-CPA secure under linear assumption. We design a generalized ElGamal scheme from the generalized linear. We also run an evaluation of performances of our scheme. We show that the decryption algorithm is slightly faster than the existing versions.