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In this paper, multi-user relay networks are considered. We formulate a multi-user relay network model where all the relay nodes amplify and forward the signals from the source nodes to the destination nodes. Then we define the metric of energy efficiency and prove the quasi-concavity of the expression for energy efficiency. Moreover, a bisection method is raised to solve the problems. Three schemes including energy efficient(EE) scheme, spectrum efficient(SE) scheme and equal power allocation(EPA) scheme are compared, and the numeral results show that the EE scheme always achieve the highest energy efficiency, meanwhile, there has been a tradeoff between the energy efficiency and spectrum efficiency in practical designs.