Abstract: Abstract: The free-piston engine has an advantage of changeable piston motion trajectory because of its lack of mechanical constraint. The motion law of a four-stroke ignited free-piston engine was studied in order to improve the efficiency of the system. Based on analyzing the working principle of the system and setting boundary constraints and path constraints of the system, an optimized model of the piston motion was established. The working cycle of the free-piston engine was composed of intake, compression, combustion, expansion and exhaust phases. Based on the characteristics of separate phase of the piston motion, a trajectory optimal method called gauss pseudospectral method (GPM) was used to separate the states and control variables. In this method, the piston position, the piston velocity, the in-cylinder gas pressure and the in-cylinder gas temperature were set as the state variables and the electromagnetic forces were set as the control variables. Then the optimal problem of piston motion was discretized to nonlinear programming problem. Then the nonlinear programming problem was solved by the sequential quadratic programming method (SQP). Furthermore, the parameters of the 462 engines were taken as the computing parameters. The fuel used in the simulation was gasoline. The simulation results showed that by adjusting the separate electromagnetic force and optimizing the piston position and velocity curves, the output work increased while the heat-transfer loss reduced with the rapid piston motion. It indicated that the efficiency reached as high as 45.3% in the simulation. During the compression process, the applied time of the optimized electromagnetic force was delayed compared with the original. And the time spent in the optimized compression process was shorter than the original. During the early expansion process，the optimized amplitude of the electromagnetic force was bigger than the original, which made the in-cylinder combustion close to constant volume combustion and the gas pressure and temperature increase quickly. During the middle expansion process, the electromagnetic force was not applied, which made the piston move fast and avoid more losses of heat transfer under the condition of high temperature and high pressure. During the late expansion process, the big electromagnetic force was applied in order to meet the target expansion length. Then comparison experiments of different piston trajectories were studied under the natural aspirate. The intake air pressure was 0.1 MPa, the temperature was 303 K and the excess air coefficient was 1.05. The results were derived from repeat experiments, which validated that the optimal method was feasible and valid. The in-cylinder peak pressure had a notable increase when the electromagnetic forces were applied by separate phase. The output electrical efficiency reached 31.2% and the system performance was remarkably improved. The output electric power had a small increase, because the cycle period was extended. As a result, the proposed optimization method of the piston motion law has an important significance for the system development.