As a major kind of query-dependent community detection, community search finds a densely connected subgraph containing a set of query nodes. As density is the major consideration of community search, most methods of community search often find a dense subgraph with many vertices far from the query nodes, which are not very related to the query nodes. Motivated by this, a new problem called community focusing (CF) is studied. It finds a community where the members are close and densely connected to the query nodes. A distance-sensitive dense subgraph structure called β-attention-core is proposed to remove the vertices loosely connected to or far from the query nodes, and a combinational density is designed to guarantee the density of a subgraph. Then CF is formalized as finding a subgraph with the largest combinational density among the β-attention-core subgraphs containing the query nodes with the largest β. Thereafter, effective methods are devised for CF. Furthermore, a speed-up strategy is developed to make the methods scalable to large networks. Extensive experimental results on real and synthetic networks demonstrate the performance of our methods.