Abstract: A constructive theorem of generalized synchronization for discrete chaos systems is established. Based on the theorem, a generalized chaotic synchronization discrete system was constructed. Combining this system with the Henon chaotic mapping designs a digital image encryption scheme, which can successfully encrypt and decrypt gray-scale images without any lost. The scheme is sensitive to perturbations of the parameters and initial conditions of the chaos system. Any perturbations which are larger than 10^-15 will make corresponding decryptions become impossible. The key space of the scheme is as large as 10⁷⁶. The analysis of key space and key parameter sensitivity shows that the scheme has sound security. Numerical simulations reveal that the scheme is effective in network communication.