A new fast successive approximation algorithm for the solution of the inverse position analysis of a general serial manipulator is presented. With the algorithm, we can search out the inverse solution of the serial manipulator quickly under the desired precision when the position of the three non-collinear end effector points is given. The position analysis of the 7R redundant serial manipulator is illustrated in the literature as an example. The simulation results verify the efficiency of the proposed algorithm. Since the three non-collinear end effector points can be selected at random, the algorithm can be applied to any other type serial manipulator.