Mobile edge computing is emerging to provide cloud-computing capabilities to mobile users, so that they can offload computation intensive tasks to close proximity for execution. However, most existing works imply that a transmission-finished task still occupies the channel until all users on the same channel finish the transmission, leading to severe channel resource waste. To solve this problem, we propose an efficient computation offloading mechanism which releases the channel resources of transmission-finished tasks for transmission-unfinished tasks, and aims to minimize the response time and energy consumption for each user. Specifically, we formulate the computation offloading problem as a game, analyze its structural properties and show how it possesses a Nash equilibrium and admits the finite improvement property, in the cases of elastic cloud and non-elastic cloud respectively. We then propose a Distributed Multi-channel Computation Offloading (DMCO) algorithm, which can converge to a Nash equilibrium, and find the upper bound of the convergence time. We further evaluate the performance of DMCO using the price of anarchy. Numerical results show that DMCO scales well with the number of users, and outperforms existing works, for example, benefits 13.3 percent more users and reduces cost by 23.7 percent than CO, one of the best existing works.