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In this paper, a cache-enabled wireless network with circuit power consumption is considered, and the strategy of joint transmission and local caching is studied. The optimization problem of energy consumption minimization is formulated, where the optimized variables include the transmission rate and the local caching rate. The constraint conditions contain the maximum data departure curve, the minimum data departure curve, and the range of the local caching rate. The original problem is intractable and is transformed into a two-layer optimization one by variable substitution. Under given caching policy, the sufficient and necessary conditions for the optimal offline transmission strategy are deduced by using the transmission characteristics. Then, an energy-efficient offline transmission strategy is proposed, and its optimality is proved. The simulation results are provided to verify the performance of the proposed strategy. The simulation results reveal the impact of the cache capacity and the file popularity on energy consumption. Under the same conditions, the performance of the proposed strategy is better than that of the other known algorithms. The proposed strategy to energy-efficient communication is helpful for future green communication.