In this paper, we analyzed the effects of carrier frequency offset for Weighted fractional Fourier transform (WFRFT) system under the time frequency fading channel. The expression of signaltointerference ratio (SIR) due to intercarrier interference (ICI) and intersymbol interference (ISI) is derived and the bit error rate (BER) performance of the BPSK modulation scheme are simulated for singlecarrier (SC), OFDM and WFRFTOFDM systems respectively. Simulation results show that when carrier offset exists, the WFRFT system has superiority over both SC and OFDM systems after choosing an optimal fractional order by experiment.