In order to improve leakage characteristic, angled-circumferential-groove pump seal is suggested. CFD analysis using FLUENT has been performed to predict leakage and determine an optimum slanted-groove angle $alpha$ which yields the best leakage reduction. The optimum value of $alpha$ ranges from $45^{circ}$ to $60^{circ}$ and depends on the pressure difference of seal and number of grooves for the same groove geometry. The maximum leakage reduction ratio increases as increasing the pressure difference of angled-circumferential-groove pump seal with the optimum value of $alpha$.