In mechanical engineering field, sealing technology is of vital importance for the success of a product. A poor sealing design of a slipper-swash plate friction pair (SSPFP) could lower the reliability of a hydraulic piston pump and lead to the failure of the pump. In this paper, a reliability-based robust design method for the sealing of the SSPFP in hydraulic piston pumps is first established. The matrix expression of the relation between the numerical characteristics of the state function of the SSPFP and the random variables is derived. Methods for calculating the sealing reliability and analyzing the reliability sensitivity of the SSPFP in the hydraulic piston pump are provided. Then, the reliability-based robust design is formulated as a multiobjective design optimization problem to meet the reliability requirements. A numerical example is presented to demonstrate performance of the proposed sealing reliability-based robust design method.