In order to optimize the distribution characteristics of the four assignment windows axial piston pump and reduce the vibration and noise during the flow distribution process, the structural parameters of the triangular damping groove were used as design variables, and the flow pulsation rate and pressure pulsation rate of the two outlets were used as optimization targets. The design variable sample points were obtained according to the Latin hypercube sampling method, and the simulation results of each sample were obtained by the fluid simulation software PumpLinx. Based on the RBF neural network, the mapping relationship between the structure parameters of the triangular damping groove and the optimization objective was constructed, and the multi-objective optimization was realized by the NSGA-Ⅱ algorithm. The results show that the predicted value of the RBF neural network model is basically consistent with the flow field simulation result. The optimal design parameters of the triangular damping groove can be obtained by this method, and the flow pulsation rate of the two ports of the piston pump is reduced by 11.3% and 11.8%, and the pressure pulsation rate is reduced by 7.6% and 10.5%.