The forward displacement analysis of parallel mechanism is attributed to find the solution of complex nonlinear equations which is a very difficult process. Taking chaotic sequences as the initial values of the damp least square method, we can find all the solutions of equations quickly. The paper investigated the initial points generated by hyper-chaotic Hénon mapping and provided a new method and calculation step of finding the all real number solutions of nonlinear equations. Using quaternion, the mathematical model of forward displacement for the generalized 4SPS-2CCS Stewart parallel robot mechanism was established and an example was given. Example showed the calculation is brief and general. It can be used in forward displacement of other parallel mechanism. The research builds the theory basis for dimensional design, trajectory planning and controlling of this type of manipulator.