Differential space-time coding was proposed recently in the literature for multi-antenna systems, where neither the transmitter nor the receiver knows the fading coefficients. Among existing schemes, double differential space-time (DDST) coding is of special interest because it is applicable to continuous fast time-varying channels. However, it is less effective in frequency-selective fading channels. This papers authors derived a novel time-frequency double differential space-time (TF-DDST)coding scheme for multi-antenna orthogonal frequency division multiplexing (OFDM) systems ina time-varying frequency-selective fading environment, where double differential space-time coding is introduced into both time domain and frequency domain. Our proposed TF-DDST-OFDM system has a low-complexity non-coherent decoding scheme and is robust for time- and frequency-selective Rayleigh fading. In this paper, we also propose the use of state-of-the-art low-density parity-check (LDPC) code in serial concatenation with our TF-DDST scheme as a channel code. Simulations revealed that the LDPC based TF-DDST OFDM system has low decoding complexity and relatively better performance.