A steering assistance control apparatus includes a positional deviation calculator, a relative yaw angle calculator, a target value calculator, and a steering driver. The positional deviation calculator calculates a lateral positional deviation between an own vehicle and a preceding vehicle, based on a detection signal by a sensor. The relative yaw angle calculator calculates a relative yaw angle, in which the relative yaw angle is an angle formed by a traveling direction of the own vehicle and a traveling direction of the preceding vehicle. The target value calculator calculates a steering-related control target value, based on the lateral positional deviation and the relative yaw angle. The steering driver that drives a steering mechanism, based on the control target value.