Selected mapping (SLM) technique is commonly employed for reducing peak to average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. Conventional SLM scheme has better spectral efficiency, but requires a bank of inverse fast Fourier transforms (IFFTs) to produce candidate signals, resulting in a dramatic increase in computational complexity. To reduce the computational complexity of the SLM technique, this paper proposes a new PAPR reduction scheme of OFDM system, called a modified fast T-transform based SLM OFDM scheme, which considerably reduces the computational complexity with better PAPR reduction performance compared to the conventional T-SLM OFDM scheme. The proposed scheme is analytically and numerically evaluated for the OFDM system specified in the IEEE 802.16d standard. For the OFDM system with 256 subcarriers, the proposed scheme can reduce the complex multiplications by 68.7 % with the lower PAPR by range of 7 dB which is about 1 dB less than the conventional SLM based OFDM.