In microwave photonic radar systems, the generation and transmission of linear frequency modulated wave (LFMW) are influenced by dispersion in the optical systems and devices. As the bandwidth of LFMW used in radar systems becomes greater, the effect of dispersion on wideband optical signal cannot be ignored and should be well compensated. Traditional compensation methods of dispersion in optical systems are facing difficulties when dealing with high order dispersion and wideband signals with demand of precise frequency control. This paper proposed a method of dispersion compensation for wideband LFMW transmission in optical systems with dispersion, based on single-side band (SSB) modulation and pre-distortion, and the linear mapping from time to frequency of LFMW. Dispersion of the transmission systems is measured to calculate the pre-distortion of LFMW. Then the single frequency laser is SSB modulated by microwave LFMW in amplitude to remove the influence from dispersion on the envelope, and the LFMW is predistorted with the calculated results in generation. In the proof-of-concept experiment, an LFMW with period of 10 us, pulse width of 8 us and instantaneous frequency from 8 GHz to 12 GHz is modulated on the laser with wave length of 1550 nm, and transmitted in dispersion fiber or devices. Second order dispersion of about 1713 ps/nm introduced by dispersion fiber is compensated in experiments. Third and fifth orders dispersion introduced by an equivalent electronic filter are compensated, and 44% improvement of the linearity of frequency modulation after compensation is obtained in the experiment.