Programmable magnetic field-free manipulation of perpendicular magnetization switching is essential for the development of ultralow-power spintronic devices. However, the magnetization in a centrosymmetric single-layer ferromagnetic film cannot be switched directly by passing an electrical current in itself. Here, we demonstrate a repeatable bulk spin-orbit torque (SOT) switching of the perpendicularly magnetized CoPt alloy single-layer films by introducing a composition gradient in the thickness direction to break the inversion symmetry. Experimental results reveal that the bulk SOT-induced effective field on the domain walls leads to the domain walls motion and magnetization switching. Moreover, magnetic field-free perpendicular magnetization switching caused by SOT and its switching polarity (clockwise or counterclockwise) can be reversibly controlled in the IrMn/Co/Ru/CoPt heterojunctions based on the exchange bias and interlayer exchange coupling. This unique composition gradient approach accompanied with electrically controllable SOT magnetization switching provides a promising strategy to access energy-efficient control of memory and logic devices.