The hyper-chaotic Newton downhill method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 33th non-plane 2-coupled–degree nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining Newton downhill method with hyper-chaotic sequences, hyper-chaotic Newton-downhill method based on utilizing hyper-chaotic discrete system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given. Comparison was also done with other finding solution method. The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.