Data mining based on data stream has become one of hot research fields. In this paper we present a novel algorithm for clustering data streams based on dynamic grids named DG-CluStream. DG-CluStream partitions and prunes grids dynamically, improves the accuracy of grids gradually through saving feature tuples of grids. The algorithm can discover clusters with arbitrary shape and is more efficient than those static methods due to a notable decrease on the number of the grids. Through fading coefficient, DG-CluStream can also deal with the problem of concept drifting efficiently. The experimental results on real datasets and synthetic datasets demonstrate promising availabilities of the approach.