A driving assistance system for a vehicle comprising: recognition means for recognizing a solid object existing in the surrounding of a driver's own vehicle and generating information about a relative position of the solid object and the driver's own vehicle; setting means for setting a grid map representing relative positions of the present location of the driver's own vehicle, an avoidance area, a safe area, and an unknown area on the basis of the information generated by said recognition means, the avoidance area being an area in which a solid object exists, the safe area being an area in which no solid object exists, and the unknown area being an area in which it is not known whether a solid object exists or not; and assistance means for, when the course of the driver's own vehicle crosses said avoidance area in the grid map set by said setting means, determining a plurality of primary paths, designating an avoidance line from among the plurality of primary paths, and changing the momentum of the driver's own vehicle in such a way that the driver's own vehicle travels along the designated avoidance line, the primary paths being paths along which the driver's own vehicle can travel by changing the momentum of the driver's own vehicle, and the avoidance line being a path along which the avoidance area can be avoided, characterized in that when said plurality of primary paths do not include an avoidance line, said assistance means sets a diverging point in said primary paths at which the momentum of the driver's own vehicle is to be changed again, determines a plurality of secondary paths, and designates an avoidance line from among the plurality of secondary paths, the secondary paths being paths along which the driver's own vehicle can travel by changing the momentum of the driver's own vehicle at said diverging point. recognition means for recognizing a solid object existing in the surrounding of a driver's own vehicle and generating information about a relative position of the solid object and the driver's own vehicle; setting means for setting a grid map representing relative positions of the present location of the driver's own vehicle, an avoidance area, a safe area, and an unknown area on the basis of the information generated by said recognition means, the avoidance area being an area in which a solid object exists, the safe area being an area in which no solid object exists, and the unknown area being an area in which it is not known whether a solid object exists or not; and assistance means for, when the course of the driver's own vehicle crosses said avoidance area in the grid map set by said setting means, determining a plurality of primary paths, designating an avoidance line from among the plurality of primary paths, and changing the momentum of the driver's own vehicle in such a way that the driver's own vehicle travels along the designated avoidance line, the primary paths being paths along which the driver's own vehicle can travel by changing the momentum of the driver's own vehicle, and the avoidance line being a path along which the avoidance area can be avoided, characterized in that when said plurality of primary paths do not include an avoidance line, said assistance means sets a diverging point in said primary paths at which the momentum of the driver's own vehicle is to be changed again, determines a plurality of secondary paths, and designates an avoidance line from among the plurality of secondary paths, the secondary paths being paths along which the driver's own vehicle can travel by changing the momentum of the driver's own vehicle at said diverging point.