Reconfigurable intelligent surface (RIS) is widely accepted as a potential technology to assist in communication between base stations (BSs) and users in edge areas. We study the energy efficiency of a RIS-assisted multi-cell communication system with a realistic RIS power consumption model. With the goal of maximizing the energy efficiency of the system, we optimize the transmit beamforming vectors at the BS and the RIS phase shift matrix by a proposed alternative optimization algorithm. First, the transmit beamforming vector is optimized by solving the transformed weighted minimum mean square error (WMMSE) problem. Subsequently, to solve the inconvenience incurred by the discrete relationship between the RIS reflecting unit power consumption and its discrete phase shift, we use a continuous function to approximate their relationship. With this approximation, we can use the majorization minimization (MM) technique to optimize the continuous RIS phase shifts, and then quantize the obtained phase shifts to discrete ones. Simulation results demonstrate that the energy efficiency of the system is effectively optimized by the proposed algorithm.