Two primary concerns in performing watershed overland flow routing are the numerical instability and computational efficiency. The stability of executing an explicit scheme has to be maintained by observing the Courant-Friedrich-Lewy criterion, which is adopted to confirm that the numerical marching speed is larger than the wave celerity. Moreover, there is another criterion of time step devised in previous studies to avoid back-and-forth refluxing between adjacent grids. The situation of refluxing usually occurs on flat regions. In light of this, the selection of a small time increment to honor both restrictions simultaneously is believed to decrease the computational efficiency in performing overland flow routing. This study aims at creating a robust algorithm to relax both restrictions. The proposed algorithm was first implemented on a one-dimensional overland plane to evaluate the accuracy of the numerical result by comparing it with an analytical solution. Then, the algorithm was further applied to a watershed for 2D runoff simulations. The results show that the proposed integrated algorithm can provide an accurate runoff simulation and achieve satisfactory performance in terms of computational speed.