Half-frequency-division duplexing (H-FDD) has recently attracted attention since it can serve as a cost-effective solution for machine-to-machine (M2M) communication networks. This letter proposes a method to jointly optimize resource allocation, mobile station grouping, and frame partitioning for H-FDD orthogonal frequency-division multiplexing access systems. We develop a near-optimal and low-complexity algorithm that is also applicable to frequency-division duplexing and time-division duplexing as special cases. Simulation results demonstrate that our algorithm with reduced computation can provide performance close to that of the optimal but time-consuming exhaustive search.