In recent years, the controllability of impulsive differential systems has attracted people's attention, and such systems have been applied in aerospace technology, information science, control system, communication, life science, medicine, economy and other fields. For this reason, the approximation controllability of a class of nonlinear fractional order impulsive differential systems is considered in Banach space. Some achievements have been made on the approximation controllability of semilinear differential systems, but the approximation controllability of impulsive differential systems is more practical significance and generalize the existing theoretical results. Firstly, the existence of the fractional impulsive differential systems mild solution is obtained by using Schauder fixed point theorem. Secondly, the approximation controllability of this type of system is studied by applying the semigroup theory and the relevant properties of the solution operators and the resolution operators. Finally, an example analysis and application is given to illustrate the main results.