For the decrease of system spectral efficiency caused by atmospheric turbulence, an adaptive modulation and coding system for atmospheric laser communication under discrete rate condition is studied. A turbulent channel model is established from the viewpoint of signal layer, and the probability density function of instantaneous signal to noise ratio in turbulent channel is presented and verified by outfield experiments. The system spectral efficiency and bit error rate formulas are derived theoretically. Simulation results indicate that the adaptive modulation and coding system for atmospheric laser communication is superior to the traditional single transmission mode system. In addition, the characteristics of spectral efficiency curves and error rate curves are studied. Influences of bit error rate requirement and turbulence intensity on system performance are analyzed. Results show that the spectral efficiency is greatly improved when we decrease the bit error rate requirement. The lower the bit error rate requirement is, the weaker the turbulence intensity is, and the higher the spectral efficiency is.