In this paper, the supercontinuum generation of picosecond pump pulses in the medical photonic crystal fibers with normal dispersion were simulated using the split-step Fourier method, and the influences of the center wavelength, peak power, width, and shape of the pump pulses on the supercontinuum characteristics were studied. Furthermore, the parameters of the pump pulse source were optimized for optical coherence tomography, improving the longitudinal resolution and imaging quality of the light source. The results show that for medical photonic crystal fibers with pump center wavelengths of 1.06 μm, 1.31 μm, and 1.55 μm, in the case of the same parameters, the 1.55 μm pump pulse generates a larger bandwidth, and the 1.31 μm pump pulse obtains a smaller longitudinal resolution. In addition, for the 1.55 μm fiber, when the peak power and width of a hyperbolic secant pump pulse are 20.5 W and 2 ps, respectively, the longitudinal resolution is 5.0 μm. Moreover, when the pulse width is 0.5 ps and the peak power is 18 W, the longitudinal resolution is 3.7 μm. Compared with the Gaussian, hyperbolic secant, and chirped Gaussian pump pulses, the super-Gaussian pump pulses can obtain a wide and flat supercontinuum light source.