The invention discloses a drive control method and device of a hybrid electric vehicle and the hybrid electric vehicle. The method comprises the following steps: obtaining the current gear of the hybrid electric vehicle and the current electric quantity of a power battery; judging whether the hybrid electric vehicle is at a speed start-stop interval according to the current gear of the hybrid electric vehicle and the current electric quantity of the power battery; if the hybrid electric vehicle is at the speed start-stop interval, further obtaining the slope of a road at which the hybrid electric vehicle is located currently and the current speed; and controlling a motor and/or an engine of the hybrid electric vehicle to work according to the slope of the road at which the hybrid electric vehicle is located currently and the current speed. By applying the drive control method of the hybrid electric vehicle disclosed by the embodiment of the invention, the recycling of the electric quantity can be increased, the mileage of the vehicle can be increased, the economic performance can be improved, the fuel consumption can be lowered, and the emissions can be reduced.