A drop-off assist device configured to be mounted on a host vehicle and comprising a processor configured to: detect an approaching object based on peripheral information obtained by a peripheral information detection device, acquire information on the approaching object including at least a relative position relative to the host vehicle, a longitudinal distance (D2_X) to the host vehicle, a relative speed (dV) of the approaching object, and a traveling direction of the approaching object, based on radio-wave information, predict a movement path of the approaching object based on the acquired information on the approaching object, issue an alarm when a movement path condition is met and a prohibition condition is not met, the movement path condition being met when the approaching object is present, the approaching object is an object that is approaching the host vehicle and of which the predicted movement path is a path along which the object passes by a door of the host vehicle; and not issue the alarm when the prohibition condition is met, even when it had previously been determined that the movement path condition was met, characterized in that, in a case where the stationary object is present, the stationary object being stationary at a side of the host vehicle, the prohibition condition includes a condition that is met when a difference acquired by subtracting a distance (D3_Y) in a transverse direction between a portion of the host vehicle on a side closer to the stationary object and a portion of the stationary object on a side closer to the host vehicle in the transverse direction, from a distance (D2_Y) in the transverse direction between a portion the host vehicle on a side closer to the approaching object and a portion of the approaching object on a side farther from the host vehicle in the transverse direction, is equal to or more than a predetermined value, the distances (D2_Y, D3_Y) being acquired by the drop-off assist device based on the peripheral information. detect an approaching object based on peripheral information obtained by a peripheral information detection device, acquire information on the approaching object including at least a relative position relative to the host vehicle, a longitudinal distance (D2_X) to the host vehicle, a relative speed (dV) of the approaching object, and a traveling direction of the approaching object, based on radio-wave information, predict a movement path of the approaching object based on the acquired information on the approaching object, issue an alarm when a movement path condition is met and a prohibition condition is not met, the movement path condition being met when the approaching object is present, the approaching object is an object that is approaching the host vehicle and of which the predicted movement path is a path along which the object passes by a door of the host vehicle; and not issue the alarm when the prohibition condition is met, even when it had previously been determined that the movement path condition was met, characterized in that, in a case where the stationary object is present, the stationary object being stationary at a side of the host vehicle, the prohibition condition includes a condition that is met when a difference acquired by subtracting a distance (D3_Y) in a transverse direction between a portion of the host vehicle on a side closer to the stationary object and a portion of the stationary object on a side closer to the host vehicle in the transverse direction, from a distance (D2_Y) in the transverse direction between a portion the host vehicle on a side closer to the approaching object and a portion of the approaching object on a side farther from the host vehicle in the transverse direction, is equal to or more than a predetermined value, the distances (D2_Y, D3_Y) being acquired by the drop-off assist device based on the peripheral information.