In recent years, space-time (ST) code has been widely applied in wireless communications. However, due to interference or signal attenuation, the performance may be degraded when the data stream is transmitted through a wireless mobile fading channel. The ST block code is an effective approach, which can provide robustness by increasing the diversity gain. In this paper, five ST-OFDM systems with different code rates are presented. Moreover, a Walsh-Hadamard (WH) transform is employed as a pre-coder to form a new WH-ST-OFDM scheme. It provides a low peak-to-average power ratio at the transmitter and a significant diversity gain at the receiver. Simulation results show that the bit error rate (BER) performance of the 4x1 ST-OFDM system with code rate 1/2 is the best among all five systems due to the highest diversity gain; and the BER of the WH-ST-OFDM system is better than that of the ST-OFDM system.