The standard Ginzburg-Landau (GL) equations are only valid in the vicinity of the critical temperature. Based on the Eilenberger equations for a single band and s-wave superconductor, we derive a modified version of the standard GL equations to improve the applicability of the standard formalism at temperature away from the critical temperature. It is shown that in comparison with previous studies, our method is more convenient to calculate and our modified equations are also compatible with a dirty superconductor. To illustrate the usefulness of our formalism, we solve the modified equations numerically and give the magnetic field distribution in the mixed state at any temperature. The results show that the vortex lattice could be still observed even away from the critical temperature (e.g., T/Tc = 0.3).