Many questions in natural science and engineering are transformed into nonlinear equations to be found. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. A composite discrete chaos dynamical system was constructed by two special discrete chaos dynamical systems and initial points were produced by proposed chaos system. For the first time, a new method based on composite discrete chaos dynamical system to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the new method is correct and effective.