With the dramatic increase of microblog users, microblog websites have become the platform for a wide spectrum of users to get information. Due to the fact that blog is a special type of text with restricted length, traditional community detection algorithms cannot effectively solve the sparse problem of micro blog. To address the issue, the DC-DTM (discovery community by dynamic topic model) algorithm is proposed in this paper. First, the algorithm maps microblog as a directed-weighted network, in which the direction is the concerned relationship, and the weight is the topic's similarity of different nodes calculated by DTM (dynamic topic model). DTM is a microblog topic model which can not only mine the topics of each microblog accurately but also calculate author's influence a topic. Second, the algorithm uses label propagation WLPA (weighted lebel propagation), with low complexity, to find communities in microblog. The initial process selects nodes with the largest influence as the initial nodes, and propagates the label in the order of node's influences, from large to small. The algorithm overcomes the adverse phenomenon in the traditional label propagation algorithm, and has better stability. Experiments on real data show that the DTM model can be very good for the topic mining in microblog and DC-DTM algorithm can effectively discover the communities of microblog.