The direct kinematics analysis is the foundation of implementation of real world application of parallel manipulators. For most parallel manipulators the direct kinematics is challenging. In this paper, for the first time a fast and efficient Homotopy Continuation Method, called the Ostrowski Homotopy continuation method has been implemented to solve the direct and inverse kinematics problem of the parallel manipulators. This method has advantage over conventional numerical iteration methods, which is not rely on the initial values and is more efficient than other continuation method and it can find all solutions of equations without divergence just by changing auxiliary Homotopy function. Numerical example and simulation was done to solve the direct kinematic problem of the 3-UPU parallel manipulator that leads to 16 real solutions. Results obviously reveal the fastness and effectiveness of this method than the conventional Homotopy continuation methods such as Newton Homotopy. The results shows that the Ostrowski-Homotopy reduces computation time up to 80-97 % with more accuracy in solutions in comparison with the Newton Homotopy.