Cellular structures are promising candidates for additive manufacturing (AM) due to their lower material and energy consumption. In this work, an efficient method is proposed for optimizing the topology of variable-density cellular structures to be fabricated by certain AM process. The method gains accuracy by relating the cellular structure's microstructure to continuous micromechanics models and achieves efficiency through conducting continuum topology optimization at macroscopic scale. The explicit cellular structure is then finally reconstructed by mapping the optimized continuous parameters (e.g., density) to cell structural parameters (e.g., strut diameter). The proposed method is validated by both finite element analysis and experimental tests on specimens manufactured by stereolithography.