Cyclic delay diversity (CDD) is considered a simple approach to exploit the frequency diversity, to improve the system performance in orthogonal frequency division multiplexing (OFDM) systems. Also, the linear precoding technique can significantly improve the performance of communication systems by exploiting the channel state information (CSI). In order to achieve enhanced performance, we propose applying linear precoding to the conventional CDD-OFDM transmit diversity schemes over Rayleigh fading channels. The proposed scheme works effectively with the accurate CSI in time-division-duplex (TDD) OFDM systems with CDD, where the reciprocity is assumed instead of channel state feedback. For a BER of $10^{-4}$ and the mobility of 3 km/h, simulation results show that a gain of 6 dB is achieved by the proposed scheme over both flat fading and Pedestrian A (Ped A) channels, compared to the conventional CDD-OFDM system. On the other hand, for a mobility of 120 km/h, a gain of 2.7 dB and 3.8 dB is achieved in flat fading and Vehicular A (Veh A) channels, respectively.