The problem synthesis of planar Stephenson Ⅲ six-link mechanism for function generation all the while is a research difficult puzzle in mechanism fields. The hyper-chaos Newton downhill method finding all real solutions of nonlinear equations was proposed that is based on utilizing hyper-chaotic discrete system to obtain locate initial points to find all real solutions of the nonlinear questions. The numerical example of synthesis of planar Stephenson Ⅲ six-link mechanism for function generation with 11 accurate points was given. The result shows that most real solutions have been quickly obtained. The number of solutions is the most and the time-spending is the less than existing any other method and it proves the correctness and validity of the proposed method.