For the laser frequency stabilization system which uses rubidium saturated absorption spectroscopy as the laser frequency reference, the loop bandwidth is one of the important facts which influence the laser output frequency noise. The main factors which limit the loop bandwidth of the laser frequency stabilization system are analyzed. Then, the radio frequency modulation signal is used to directly modulate the high speed current modulation port of the commercial external cavity diode laser, and the loop bandwidth of the laser frequency stabilization system is expanded. According to the analysis of the frequency stabilization loop, the feedback circuit is set up to realize the laser frequency stabilization. After analyzing the error signal of stabilized laser by low frequency spectrum analyzer, it is found that the frequency noise suppression can be improved to be larger than 20 dB at the Fourier frequency of 5 kHz. The beat frequency is conduct between laser from stabilized frequency laser and femtosecond optical frequency comb locked on ultra-stable oven controlled crystal oscillator, and the frequency noise of stabilized laser is also measured. The results are consistent with the analyzing results of the error signal. The frequency noise is suppressed when we expand the bandwidth, and the short-term frequency stability of the stabilized frequency laser is improved. Finally, the frequency stability of stabilized frequency laser relative to OCXO referenced femtosecond optical frequency comb is measured. It can reach to 4.52×10-12 at averaging time of 1 s and reach to 1.65×10-12 at averaging time of 20 s.