Abstract: Considering the strong discontinuities appeared in the solutions of hyperbolic conservation law equations with the development of time and the ability of pseudo arc-length method (PALM) in weakening the singularity of the equation, a high-order PALM was developed based on the combination of the PALM and the high-order weighted essentially non-oscillatory (WENO) scheme to effectively improve the accuracy and resolution of the calculation. To overcome the complexity of a high-order scheme construction in the deformed mesh, a coordinate transformation method was adopted to make the governing equation mapped to the orthogonal uniform arc-length space, completing the calculation in the arc-length space. Combined with Level Set technology and real ghost fluid method (RGFM) interface processing, the algorithm was extended to the calculation of multi-medium flows. For the interpolation of Level Set distance function after grid movement, a third-order non-conservative interpolation scheme was proposed. The results show that the high-order PALM has high convergence order, which can effectively reduce the numerical oscillation at the discontinuity and improve the discontinuity resolution.