This article addresses the multicast resource allocation problem with min-rate requirement constraints in orthogonal frequency division multiplexing (OFDM) systems. Due to the prohibitively high complexity for nonlinear and combinatorial optimization, the original problem is relaxed and reformulated to form a standard optimization problem. By theoretical derivation according to the Karush-Kuhn-Tucker (KKT) conditions, two propositions are presented as the necessary criteria for optimality. Furthermore, a two-step resource allocation scheme, including subcarrier assignment and power allocation, is proposed on a basis of the propositions for practical implementation. With the min-rate based multicast group order, subcarriers are assigned in a greedy fashion to maximize the capacity. When subcarrier assignment is determined, the proposed power allocation can achieve the optimal performance for the min-rate constrained capacity maximization with an acceptable complexity. Simulation results indicate that the proposed scheme approximates to optimal resource allocation obtained by exhaustive search with a negligible capacity gap, and considerably outperforms equal power distribution. Meanwhile, multicast is remarkably beneficial to resource utilization in OFDM systems.