Adaptive modulation and coding (AMC) provides the flexibility to match modulation and coding scheme (MCS) to signal to interference plus noise ratio (SINR) of users. To reduce the transmission power and maintain the transmission quality, power control is normally combined with AMC. While the target SINR of power control is fixed, therefore non-cooperative power control game for AMC (NPGA) algorithm was proposed to adapt to the dynamic target SINR changes according to MCS. In NPGA, we formulate system transmission efficiency via utility, where the utility function is constructed based on the modulation and coding efficiency with non-cooperative game theory. It is demonstrated theoretically that NPGA can satisfy the conditions of the supermodular games, and its solution is optimal. The simulation results show that NPGA can improve system transmission efficiency and signal quality with low transmission power, and the convergence performance of NPGA is more fast-effectiveness compared with geometric programming algorithms.