A general scheme of complete coverage for mobile robot under unknown static environment is presented. The complete coverage problem is divided into three subproblems called region decomposition, complete coverage of subregion and subregion linking separately. Boustrophedon decomposition method was used to decompose the region, and roundabout sweeping with forward steering combining with stream function for obstacles avoidance were adopted to complete coverage of subregion. The subregion linking was realized by point stabilization based on fuzzy logic control. Simulated coverage experiments were conducted under different conditions in Microsoft Robotics Studio and simulation results demonstrate the effectiveness and robustness of the proposed scheme.