Abstract: We consider a class of anti-periodic boundary value problems of semilinear fractional impulsive differential equation with p-Laplacian operator. Firstly, the fractional differential equation is transfromed into equivalent integral equation. Secondly, we are devoted to the existence and uniqueness of solution for the boundary value problem by utilizing Schauder fixed-point theorem, Schaefer's fixed-point theorem, and Banach compression mapping principle. Finally, examples are given to illustrate the main results.