We report on the efficient spin-orbit torque (SOT) switching in a single ferromagnetic layer induced by a new type of inversion asymmetry, the composition gradient. The SOT of 6- to 60-nm epitaxial FePt thin films with a $L{1}_{0}$ phase is investigated. The magnetization of the FePt single layer can be reversibly switched by applying electrical current with a moderate current density. Different from previously reported SOTs which either decreases with or does not change with the film thickness, the SOT in FePt increases with the film thickness. We found the SOT in FePt can be attributed to the composition gradient along the film normal direction. A linear correlation between the SOT and the composition gradient is observed. This Rapid Communication introduces a platform to engineer large SOTs for lower-power spintronics.