This letter introduces a resource allocation scheme in Orthogonal Frequency Division Multiplexing(OFDM) multi-cast systems which focuses on minimizing power consumption. By allocating the resource optimally, the number of OFDM symbols that each Mobile Station(MS) receives can be minimized, resulting in the reduced power consumption of MSs. A heuristic algorithm for allocating resources suboptimally with low complexity is also proposed, and is shown to achieve almost optimal performance.