In this work, the explicit formulations of the Grad's distribution function for 13 moments (G13)-based gas kinetic flux solver (GKFS) for simulation of flows from the continuum regime to the rarefied regime are presented. The present solver retains the framework of GKFS, and it combines some good features of the discrete velocity method (DVM) and moment method. In the G13-GKFS, the macroscopic governing equations are first discretized by the finite volume method, and the numerical fluxes are evaluated by the local solution of the Boltzmann equation. To reconstruct the local solution of the Boltzmann equation, the initial distribution function is reconstructed by the Grad's distribution function for 13 moments, which enables the G13-GKFS to simulate flows in the rarefied regime. Thanks to this reconstruction, the evolution of distribution function is avoided, and the numerical fluxes can be expressed by explicit formulations. Therefore, the computational efficiency of G13-GKFS is much higher than that of DVM. The accuracy and computational efficiency of the present solver in explicit form are examined by several numerical examples. Numerical results show that the present solver can predict accurate results for flows in the continuum regime and reasonable results for flows in the rarefied regime. More importantly, the central processing unit time of the present solver is about 1% of that of DVM for two-dimensional (2D) microflow problems, and it is about twice of the conventional Navier–Stokes solver for 2D continuum flows.