This article offers a method to realize the synchronization of non-symmetrically nonlinear-coupled chaotic systems, studies the chaotic synchronization of Chen's chaotic attractors, and analyzes the influence of chaotic synchronization by numerical simulation under different coupling strengths and different initial conditions. We also extend the synchronization method of non-symmetrically nonlinear-coupled systems to the study of large network linked by numerous Chen's attractor system units by all-to-all-coupling and star coupling. We deduced the equation of errors which ensures the stability of synchronous state, studied the influence of different coupling strengths on synchronization stability and determined the range of coupling strengths which ensures the synchronization. By numerical simulation we proved that if we choose nonlinear functions as coupling functions, it effectively realizes the synchronization of all-to-all-coupling network and large network linked from star sub-networks. We can foresee that the non-symmetrically nonlinear-coupled synchronization method could be widely used in network synchronization.