A novel space-time-frequency (STF) trellis coding scheme is developed for multi-antenna OFDM transmissions over frequency-selective Rayleigh fading channels. Incorporating sub-carrier grouping and choosing appropriate system parameters, we first convert our system into a set of group STF (GSTF) systems. This enables simplification of STF block coding within each GSTF system. We derive design criteria for STF trellis coding, and exploit existing ST trellis coding techniques to construct STF trellis codes. The resulting codes are shown capable of achieving maximum diversity gains, while affording low-complexity decoding. The performance merits of our design is confirmed by corroborating simulations, and compared with existing alternatives.