A systematic method for the forward kinematics of a five degrees of freedom (5-DOF)parallel mechanism with the legs'topology 4-UPS/UPU,is developed.Such mechanism is composed of a movable platform connected to the base by four identical 6-DOF active limbs plus one active limb with its DOF being exactly the same as the specified DOF of the movable platform.Three translational and two rotational DOFs can be achieved.Firstly,a set of polynomial equations of forward position analysis is formulated based on the architecture of the mechanism.Then the system of equations is degraded from five-dimensional to three-dimensional by means of analytic elimination.Method of least squares and Gauss-Newton algorithm are used to construct the objective function and to solve it,respectively.Example shows that through 4-time iteration within 16 ms the objective function converges to the provided error tolerance,10 -4.