Recently, community search over graphs has attracted significant attention and many algorithms have been developed for finding dense subgraphs from large graphs that contain given query nodes. In applications such as analysis of protein protein interaction (PPI) networks, citation graphs, and collaboration networks, nodes tend to have attributes. Unfortunately, previously developed community search algorithms ignore these attributes and result in communities with poor cohesion w.r.t. their node attributes. In this paper, we study the problem of attribute-driven community search, that is, given an undirected graph $G$ where nodes are associated with attributes, and an input query $Q$ consisting of nodes $V_q$ and attributes $W_q$, find the communities containing $V_q$, in which most community members are densely inter-connected and have similar attributes. We formulate our problem of finding attributed truss communities (ATC), as finding all connected and close k-truss subgraphs containing $V_q$, that are locally maximal and have the largest attribute relevance score among such subgraphs. We design a novel attribute relevance score function and establish its desirable properties. The problem is shown to be NP-hard. However, we develop an efficient greedy algorithmic framework, which finds a maximal $k$-truss containing $V_q$, and then iteratively removes the nodes with the least popular attributes and shrinks the graph so as to satisfy community constraints. We also build an elegant index to maintain the known $k$-truss structure and attribute information, and propose efficient query processing algorithms. Extensive experiments on large real-world networks with ground-truth communities shows the efficiency and effectiveness of our proposed methods.