Mobile cloud computing(MCC) combines mobile Internet and cloud computing to improve the performance of mobile applications. However, MCC faces the problem of energy efficiency because of randomly varying channels. A scheduling algorithm is proposed by introducing the Lyapunov optimization, which can dynamically choose users to transmit data based on queue backlog and channel statistics. The Lyapunov analysis shows that the proposed scheduling algorithm can make a tradeoff between queue backlog and energy consumption in the channel-aware mobile cloud computing system. The simulation results verify the effectiveness of the proposed algorithm. However, MCC faces the problem of energy efficiency because of randomly varying channels. A scheduling algorithm is proposed by introducing the Lyapunov optimization, which can optionally choose users to transmit data based on queue backlog and channel statistics. The Lyapunov analysis shows that the proposed scheduling algorithm can make a tradeoff between queue backlog and energy consumption in the channel-aware mobile cloud computing system. The simulation results verify the effectiveness of the proposed algorithm.