Vehicle Traveling Control Method and Traveling Control Device

When a subject vehicle performs first autonomous lane change control from a subject vehicle lane to an adjacent lane and then consecutively perform autonomous lane change control to a next adjacent lane in the same direction of lane change, lateral speed to perform second and subsequent autonomous lane change control is set slower than lateral speed to perform the first autonomous lane change control. Thus, the second and subsequent autonomous lane change control to the adjacent lane in the same direction of lane change is performed more slowly than the previously performed autonomous lane change control. Time used for confirming surrounding situations is lengthened, and the surrounding situations can be properly confirmed prior to the lane change.