Existing works have addressed the interference mitigation by any two of the three approaches: link scheduling, power control, and successive interference cancellation(SIC). In this paper, we integrate the above approaches to further improve the spectral efficiency of the wireless networks and consider the max-min fairness to guarantee the transmission demand of the worst-case link. We formulate the link scheduling with joint power control and SIC(PCSIC) problem as a mixed-integer non-linear programming(MINLP), which has been proven to be NP-complete. Consequently, we propose an iterative algorithm to tackle the problem by decomposing it into a series of linear subproblems, and then the analysis shows that the algorithm has high complexity in the worst case. In order to reduce the computational complexity, we have further devised a two-stage algorithm with polynomial-time complexity. Numerical results show the performance improvements of our proposed algorithms in terms of the network throughput and power consumption compared with the link scheduling scheme only with SIC.