Social networks are typical attributed networks with node attributes. Different from traditional attribute community detection problem aiming at obtaining the whole set of communities in the network, we study an application-oriented problem of mining an application-aware community organization with respect to specific concerned attributes. The concerned attributes are designated based on the requirements of any application by a user in advance. The application-aware community organization w.r.t. concerned attributes consists of the communities with feature subspaces containing these concerned attributes. Besides concerned attributes, feature subspace of each required community may contain some other relevant attributes. All relevant attributes of a feature subspace jointly describe and determine the community embedded in such subspace. Thus the problem includes two subproblems, i.e., how to expand the set of concerned attributes to complete feature subspaces and how to mine the communities embedded in the expanded subspaces. Two subproblems are jointly solved by optimizing a quality function called subspace fitness. An algorithm called ACM is proposed. In order to locate the communities potentially belonging to the application-aware community organization, cohesive parts of a network backbone composed of nodes with similar concerned attributes are detected and set as the community seeds. The set of concerned attributes is set as the initial subspace for all community seeds. Then each community seed and its attribute subspace are adjusted iteratively to optimize the subspace fitness. Extensive experiments on synthetic datasets demonstrate the effectiveness and efficiency of our method and applications on real-world networks show its application values.