Mobile edge computing (MEC) is becoming a promising paradigm of providing cloud computing capabilities to the edge network, which can serve mobile devices (MDs) with computation-intensive and delay-sensitive tasks. Facing with high requirements of many MDs, it’s essential for MEC with limited computation capacity to serve more MDs with QoS. For each mobile device, it is also desirable to have a low energy consumption with an expected deadline. To solve above problems, we propose a Game-based Computation Offloading (GCO) algorithm, which includes the task offloading profile and the transmission power controlling with the method of non-cooperative game. Our mechanism maximizes the number of served MDs with deadline, as well as minimizing the energy consumption of each MD whose task is executed on MEC. Specifically, Given the allocation of transmission power, a Greedy-Pruning algorithm is proposed to determine the number of tasks executed on MEC. Besides, each MD adopts his/her transmission power controlling strategy to compete the computation resource of MEC or minimize the energy consumption. A game model for illustrating the problem of task offloading is formulated to find a proper transmission power for each task and is proved the existence of Nash equilibrium solution. Experiments are simulated to evaluate the proposed algorithm in terms of effectiveness evaluation.