A high order coupled nonlinear Schrdinger equation suitable for ultra-short Airy pulses is solved by means of the split-step Fourier transform method, and the evolution of the interaction of ultra-short Airy pulses propagating in fibers is numerically simulated by Matlab software. The results show that the negative third-order dispersion effect accelerates the penetration of wave packets and makes ultra-short pulses propagate over a long distance. In contrast, the positive third-order dispersion effect slows down the propagation of ultra-short pulses, and if the third-order dispersion coefficient is large enough, the pulse oscillation is transferred from the leading edge to the trailing edge. The self-steepening effect makes ultra-short pulses generate time-domain shift in the form of soliton splitting. The intra-pulse Raman scattering effect results in a Raman self-frequency shift at the long wavelength side of the pulse, so that it can transfer the pulse energy from the leading edge to the trailing edge. Under the combined impact of the self-steepening effect and the intra-pulse Raman scattering effect, an ultra-short pulse shows a time-domain displacement and the energy at its leading edge is transferred to its trailing edge. The simultaneous existence of three effects of third-order dispersion, self-steepening and intra-pulse Raman scattering strongly influences the self-bending and self-acceleration characteristics possessed by the interaction between ultra-short Airy pulses.