The rhombic drive of Stirling engine has been designed in the article, and motion analysis have been carried out according with the requirements of mechanism design in structure. The kinematics mathematical models have been established for rhombic mechanism and the simulation analyses have been carried with the three-dimensional software for the rhombic drive. It makes a point out the optimum position relationship among the link of the rhombic drive during the four processes of the Stirling cycle, and has conducted a mathematical description of piston displacement, velocity and acceleration which drove by the rhombic drive. The simulation curves have showed the relative relationship of position, velocity and acceleration between the two pistons during the body movement. Based on these researches constructive ideas have been offered to improve the rhombic drive in the paper and laid the root for the optimal design of the Stirling engine in theory.