This study focuses on the scene that a vehicle overtakes a pedestrian in a narrow road in an urban area and proposes the safety index that shows the appropriate driving behavior in the target scene. Moreover, this study evaluates the validity of the index by experiments.In the target scenes, drivers need to drive carefully, preparing for the latent risk that the pedestrians may start crossing the roads suddenly. In other word, the vehicles must reduce the speed in order to be ready to avoid accidental contacts with pedestrians in case the pedestrians start crossing the road suddenly. However, according to the pedestrian model proposed by the authors in the previous study, the crossing angles of pedestrians are unpredictable. Therefore, the drivers must drive with such speed that the vehicle can avoid an accidental contact by braking even if the pedestrian start crossing the road at any angle. The maximum vehicle speed that satisfies above condition is formulated from velocities and positions of the vehicle and the pedestrian, and this paper proposes the maximum vehicle speed as a safety index for overtaking a pedestrian in a narrow road.Experiments are performed to evaluate the validity of the proposed maximum vehicle speed as the safety index. By comparing the safety index and the speed data of the real-car experiments, the validity of the safety index is shown.