We present an improved Gas Kinetic Flux Solver (GKFS) designed for efficient and accurate simulations of supersonic gas flows across both continuum and rarefied regimes. The key advancement is the implementation of a rescaled Gauss-Hermite quadrature in velocity space, enabling an adaptive velocity discretization that dynamically adjusts quadrature points based on local flow characteristics. This strategy significantly enhances computational efficiency while maintaining high accuracy in supersonic and moderately rarefied flows. Numerical results for 1D shock waves demonstrate that the improved GKFS achieves excellent agreement with analytical solutions using fewer quadrature points. Furthermore, the solver successfully captures flow structures in 2D oblique shock waves, supersonic rarefied flow past a circular cylinder, and NACA0012 airfoil test cases, showing remarkable consistency with reference solutions. These findings highlight the solver's potential for robust and efficient simulations in high-speed rarefied gas dynamics.