A parking assist apparatus comprising: a distance obtaining portion that obtains a movement distance from a current position (Na) of a vehicle to a parking target position; a vehicle speed calculating portion that calculates a target vehicle speed with a lapse of time until the vehicle reaches the parking target position, based on the movement distance, and a vehicle speed and acceleration and deceleration which are set in advance; a position calculating portion that calculates a movement target position (Nb) of the vehicle in accordance with the time until the vehicle reaches the parking target position, based on the target vehicle speed with the lapse of time; and a controller that controls a vehicle running state such that the vehicle is moved to the movement target position at the target vehicle speed, characterized in that in a case where the controller determines that running of following the movement target position is not possible based on the current position of the vehicle and the movement target position, if a running operation of the vehicle is detected, the controller stops a control of the vehicle running state, and if the running operation is not detected, the controller continues the control of the vehicle running state in accordance with the target vehicle speed which is corrected in accordance with a following state with respect to the movement target position of the vehicle; and in a case where a divergence between the current position of the vehicle and the movement target position is a predetermined first divergence value or more, in a case where driving force of the vehicle reaches a first driving force value which is allowed in parking assist, and in a case where braking force is not generated in the vehicle, the controller determines that the vehicle is not capable of running of following the movement target position. a distance obtaining portion that obtains a movement distance from a current position (Na) of a vehicle to a parking target position; a vehicle speed calculating portion that calculates a target vehicle speed with a lapse of time until the vehicle reaches the parking target position, based on the movement distance, and a vehicle speed and acceleration and deceleration which are set in advance; a position calculating portion that calculates a movement target position (Nb) of the vehicle in accordance with the time until the vehicle reaches the parking target position, based on the target vehicle speed with the lapse of time; and a controller that controls a vehicle running state such that the vehicle is moved to the movement target position at the target vehicle speed, characterized in that in a case where the controller determines that running of following the movement target position is not possible based on the current position of the vehicle and the movement target position, if a running operation of the vehicle is detected, the controller stops a control of the vehicle running state, and if the running operation is not detected, the controller continues the control of the vehicle running state in accordance with the target vehicle speed which is corrected in accordance with a following state with respect to the movement target position of the vehicle; and in a case where a divergence between the current position of the vehicle and the movement target position is a predetermined first divergence value or more, in a case where driving force of the vehicle reaches a first driving force value which is allowed in parking assist, and in a case where braking force is not generated in the vehicle, the controller determines that the vehicle is not capable of running of following the movement target position.