In view of the contradiction between high resolution requirements and computational efficiency faced by traditional numerical methods in multi-scale problems of hyperbolic equations, as well as the problems of insufficient cross-scale convergence and difficulty in coordinating numerical dissipation and dispersion characteristics in existing entropy-stabilized formats in complex scale coupling scenarios, this paper proposes an improved strategy for high-order entropy-stabilized algorithms based on a multi-resolution analysis framework. First, by constructing a flux limiter with an adaptive weight adjustment mechanism, a dynamic balance between shock wave capture accuracy and entropy stability characteristics is achieved. Then, a multi-scale Eigen decomposition technique based on wavelet threshold shrinkage is introduced. Finally, an integrated solution framework with spatiotemporal adaptability is designed by combining the implicit-explicit hybrid time discretization method. In the L2 error analysis experiment, the error of the improved algorithm is 42–65% lower than that of the traditional method. In the computational efficiency comparison experiment, the computational time of the improved algorithm is significantly superior under high-resolution grids. The results of the entropy stability verification experiment show that the entropy value of the improved algorithm changes little, remaining between 0.19 and 0.39. In the above data conclusions, the algorithm studied in this paper effectively improves the computational efficiency while ensuring high accuracy, and maintains good entropy stability, which is suitable for complex cross-scale physical system simulations.