The Maximum Clique is the most compact cohesive subgroup in Social Network. Finding the maximum clique in the Social Network has become an important aspect of social network analysis, such as privacy protection, citation and co-citation analysis, cohesive subgroup analysis et al. With the development of big data, the mass of nodes in the graph and complexity of analysis set a higher requirement for solving the maximum clique problem (MCP). Therefore, we propose an improved ant colony algorithm. Particularly, the strategy of the ant to select the nodes is improved so that the search space can be expanded and the variety of the solution is increased, with this approach local optimal solution can be avoided. Local improvement of the clique is also adopted to improve the accuracy and convergence speed of the proposed algorithm. The proposed algorithm has been tested on the DIMACS benchmark dataset and several typical social networks. Experimental results show the effectiveness and feasibility of the proposed algorithm.