Abstract In reversible pump-turbines at pump mode, local flow separation on the leading-edge overlaps the impeller's low-pressure side and causes a sudden pressure-drop. Hence, cavitation easily incepts on leading-edge especially at off-design conditions. To solve this cavitation problem, a NACA0006 profile was used as a simplified model of pump-turbine impeller blade to understand the cavitation inception mechanism. Numerical results indicate multiple favorable-pressure-gradients, which were caused by the quickly-varied geometry, on the hydrofoil surface. The minimum pressure occurs in one of these gradients' region and usually locates around leading-edge because of the quickly-varied geometry of leading-edge arc. Then, Diffusion-angle Integral design method was developed to design the blade leading-edge shape. It has only three design parameters by effective geometry deconstruction. Based on orthogonal test, the reasonable values of design parameters can be determined. With optimal design parameters, the NACA0006 foil and pump-turbine impeller blade were completely redesigned and improved. The inception cavitation number of the redesigned foil was obviously reduced especially at large incidence angles. The redesigned pump-turbine also has a reduced inception cavitation number and delayed cavitation inception especially at off-design conditions. The design concept, method and application in this study provide useful reference for anti-inception-cavitation design of turbomachinery blades.