In this study, a numerical model of the fuel leakage rate in the plunger-sleeve clearance of high-pressure common rail system was established based on graph theory. The transient clearance changes caused by the elastic deformation and the physical properties of the fuel along the flow direction within the plunger-sleeve were considered. This model realized the fluid–structure–thermal transient coupling during the leakage, and the accuracy was verified by comparing the calculated fuel leakage rate with the experimental data. Based on the main structural parameters of the plunger-sleeve, a three-level five-factor experimental calculation matrix was proposed using the D-optimal design method. The fuel leakage rates of all groups in the calculation matrix were obtained based on the fuel leakage rate numerical model, and the significant influencing parameters of the fuel leakage rate were determined using analysis of variance (ANOVA). The results indicate that the plunger diameter, sleeve external diameter, plunger-sleeve initial clearance and sealing length are significant parameters that affect the fuel leakage rate. In case of interaction between parameters, the interaction between the plunger diameter and sleeve external diameter, plunger diameter and plunger-sleeve initial clearance, and plunger diameter and plunger-sleeve sealing length contributed to a significant change in the fuel leakage rate. The influencing behavior of significant single parameters and significant interactions between parameters on the fuel leakage rate were revealed. The research outcomes can provide theoretical support for the optimization of the design of plunger-sleeve.