When there is a saturated intersection on the arterial road, it is necessary to intercept and regulate the traffic flow in the entry direction of the saturated intersection, so as to avoid the overflow of the section queue, and to conduct green wave dredging in the exit direction of the saturated intersection to facilitate the rapid departure of traffic flow. According to the coordination control requirements in different directions of saturated intersection, this paper proposed an algebraic method of coordination design for bi-directional red and green waves on arterial roads. Firstly, the general formula for calculating the ideal intersection distance was derived by using the time-space diagram, and the calculation method of bias-split for the coordinated phase was given. Secondly, for different common signal cycles, the bias-split for the coordinated phase under different signal phase modes of each intersection was calculated respectively. The signal phase mode corresponding to the bias-split with the smallest absolute value was taken as the preferred phase of each intersection. Then, the max difference of bias-split corresponding to the preferred phase under different common signal cycles was compared, and the common signal cycle with the minimum of the max difference of bias-split was selected as the best common signal cycle. Finally, based on the characteristics of red and green waves, the optimization method of fine-tuning signal offsets was given to minimize the bias-split of the green wave direction, so as to ensure that the arterial road can obtain bi-directional red and green wave bandwidth as wider as possible. The case analysis shows that, compared with the scheme of bi-directional green wave coordinated control, the bi-directional red and green waves coordinated control scheme designed by this method can significantly increase the green wave bandwidth in the direction of leaving the saturated intersection while ensuring that there is a maximum red wave bandwidth in the direction of entering the saturated intersection. The VISSIM simulation experiment shows that the scheme designed by this method can not only shorten the maximum queue length by 23.1% and the average queue length by 33.8%, and delay the time of vehicles queuing to overflow to the upstream intersection, but also reduce the travel time and the number of stops of the vehicles leaving at the saturated intersection in the downstream section by 17.5% and 76.3%, respectively. It can realize the overflow prevention and green wave dredging of the saturated intersection.