The forward displacement analysis of parallel mechanism is transformed into find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of the three-step iterative method, we can find all the solutions of equations quickly. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the three-step iterative method based on Chaos sequences. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 3SPS-3CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic three-step iterative method to find solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.