The supercontinuum generation and manipulation of Airy-Gaussian pulses in a photonic crystal fiber with three zero-dispersion points are studied using the split-step Fourier method. Firstly, the spectral evolution of Airy-Gaussian pulses in four photonic crystal fibers with different barrier widths was discussed, and the optimal fiber was determined after considering the factors of width and flatness. By analyzing the mechanism of supercontinuum generation in photonic crystal fibers with single, double and three zero-dispersion points, it is found that the photonic crystal fiber with three zero-dispersion points have a larger spectral width due to the component of tunneling solitons. Then, the effects of four characteristic parameters (truncation factor a, distribution factor χ0, initial chirp C and central wavelength λ) on forming the supercontinuum spectrum of Airy-Gaussian pulses are analyzed in detail. The results show that the spectral width and energy intensity of the dispersive wave and tunneling soliton generation can be well controlled by adjusting the barrier width and initial parameters of the pulse. These research results provide a theoretical basis for generating and manipulating high-power mid-infrared supercontinuum sources.