A new type of two-dimensional piston pump with magnetic motion converters is proposed, which uses a pair of magnetic motion converters capable of generating a periodic axial force to replace the original roller-cam rail two-dimensional converters of the pump. By establishing the analytical model of the magnetic motion converters, the motion law of the two-dimensional piston under the magnetic motion converters is analyzed, and the efficiency model of the pump is established according to the principle of pump. The magnetic field simulation model of the magnetic motion converters is established based on Maxwell, and the simulation model of the piston pump is established based on AMESim. The simulation results verify the validity of the analytical model. The prototype pump and test rig were built, and the volumetric efficiency and mechanical efficiency of the pump under various working conditions were obtained. The deviation between the test results and the simulation results was less than 5%, which verified the correctness of the theoretical analysis.