In this paper, we investigate the complete controllability for abstract measure differential systems. Firstly, we introduce several new concepts about complete controllability for abstract measure differential systems. Then, on the basis of the Sadovskii fixed-point theorem, we give sufficient conditions for complete controllability for a class of abstract measure differential systems. The compactness of the semigroup generated by some operator is unnecessary in this paper, and we show that our results, dealing with complete controllability problem for an ordinary differential system in infinite-dimensional Banach space, are also less conservative than that in the previous literature. Copyright © 2012 John Wiley & Sons, Ltd.