A catheter based fiber polarization-sensitive optical coherence tomography (PS-OCT) system has significant advantages in quantitative analysis of cardiovascular plaques. A dual polarization state catheter based PS-OCT system is established based on polarization maintaining fibers (PMFs) with imaging depth multiplexing. Due to the strong birefringence dispersion of PMFs, it is difficult to use a set of dispersion coefficients to realize the dual-input-state dispersion compensation. In order to solve this problem, this paper proposes a dual-state numerical dispersion compensation method for the catheter based PS-OCT system. This method can adjust dispersion coefficients of different input polarization states to compensate for the difference in dispersion of different input polarization states caused by the birefringence dispersion of the polarization maintaining fiber. Experimental results show that the proposed method can effectively solve the problems such as pulse broadening, image blurring, and poor polarization contrast caused by material dispersion and birefringence dispersion, which ensures high-quality phase retardation imaging of biological samples in the catheter based PS-OCT.