Based on the Nagel-Schreckenberg model, a traffic model for an arterial road with equal-distance-distributed intersections is established. The traffic flow is numerically simulated under the open boundary condition and the control of red and green lights. It is found from the results that the capacity of the arterial road is determined by the capacity of the intersection. For small densities, the flow has no relation with the number of intersections. Moreover, the rule of variation of the maximum point of average velocity with the green-light period is obtained with the mean-field method. On the contrary, the number of intersections plays a crucial role in the flow at larger densities. The arterial road can achieve optimal traffic state via regulating the period of traffic lights.