Abstract: The traditional lattice Boltzmann method (LBM), especially the classic single-relaxation model (SLBM) based on the uniform square grid, has poor robustness and numerical stability, which limits the development and applications of LBM. Grid refinement strategy can effectively alleviate this dilemma, however for the traditional LBM, the grid refinement will inevitably lead to a sudden drop in computational efficiency and a rise in equipment requirements. Therefore, in order to solve this problem, based on the non-uniform rectangular grid, combined with the idea of interpolation LBM, the 25-bit Lagrangian interpolation LBM is proposed on the premise of ensuring the local grid refinement for the surfaces and area with severe flow changes, and the computational accuracy as well. Taking the classic lid-driven cavity flow for instance, a comparative analysis including different grid resolutions and interpolation schemes is performed. The verification includes both the numerical simulations of steady states and unsteady periodic solutions. The results show that the Lagrangian interpolation scheme performs better than other interpolation schemes. In this paper, the local grid refinement is able to ensure the capture of the flow details adjacent to surfaces and in the area of intense flow changes. The numerical algorithm can provide reliable results for numerical simulations. Meanwhile, the total grid number is greatly reduced, as a result the computational efficiency is greatly improved; The numerical simulation method has good robustness and is suitable for numerical simulations for both steady states and unsteady solutions.