It is important to find a precise and fast algorithm for solar radiative transfer in the atmosphere . In this paper, we present, based on Stamnes's discrete-ordinate-method, an analytical four-stream approximation algorithm. In our algorithm, we separate out the singly scattered radiation and apply the normal four-stream approximation of Stamnes's discrete-ordinate-method to the multiply scattered radiation alone. The singly scattered irradiance is computed analytically without approximation, preserving more of the angular dependence in the radiance than other four-stream approximation solutions. Because of the analytical form of the derived solution, the computational time of our algorithm is less than that of the rigorous numerical algorithm. Numerical experiments show that the accuracy of the algorithm is satisfactory. Particularly in the case the absorption is dominant, the error of the algorithm is very small.