2UPS-RPU is a new 4-DOF parallel mechanism with serial input limb. In this paper, the inverse dynamic equation of this mechanism is formulated by Newton-Euler formation based on each limb and moving platform as the studying objects. The inverse kinematics of the mechanism is analyzed. The driving force, driving moment and the constraint moment can be obtained. Finally, a computer simulation is carried out to solve the inverse dynamics of the mechanism when the motion of moving platform is given.