A sheet post-processing apparatus which is capable of shortening time wasted until actual start of punching and enhancing productivity. A drive unit causes a moving member which has a cam and reciprocates. A punching member is driven by a movement of the cam of the moving member and punches a sheet when the moving member moves forth and moves back. A determination unit determines a type of the sheet. A control unit controls, when a sheet to be punched is to be subjected to a punching process, the drive unit such that the moving member starts moving before conveyance of the sheet to be punched stops, and controls, when the sheet to be punched is to be subjected to the punching process, the drive unit such that timing with which the moving member starts moving is changed based on the determination by the determination unit.