Community search is a derivative of community detection that enables online and personalized discovery of communities and has found extensive applications in massive real-world networks. Recently, there needs to be more focus on the community search issue within directed graphs, even though substantial research has been carried out on undirected graphs. The recently proposed D-truss model has achieved good results in the quality of retrieved communities. However, existing D-truss-based work cannot perform efficient community searches on large graphs because it consumes too many computing resources to retrieve the maximal D-truss. To overcome this issue, we introduce an innovative merge relation known as D-truss-connected to capture the inherent density and cohesiveness of edges within D-truss. This relation allows us to partition all the edges in the original graph into a series of D-truss-connected classes. Then, we construct a concise and compact index, ConDTruss, based on D-truss-connected. Using ConDTruss, the efficiency of maximum D-truss retrieval will be greatly improved, making it a theoretically optimal approach. Experimental evaluations conducted on large directed graph certificate the effectiveness of our proposed method.