In this paper, a novel method for image encryption based on a Generalized Chinese Remainder Theorem (GCRT) is presented. The proposed method is based on the work developed by Jagannathan et al. Some modifications are proposed in order to increase the method's encryption quality and its robustness against attacks. Specifically, the inclusion of a vector to reduce the segment pixel space and a Generalized Chinese Remainder Theorem (GCRT) algorithm are proposed. These vectors are generated randomly which allows its use as private keys joining these unrestricted key values generated by the GCRT algorithm.  An analysis to study a system where the RGB channels are independently encrypted is performed. Some experiments were carried out to validate the proposed model obtaining very promising results.