The present disclosure provides a drive control method and a drive control device of a hybrid electric vehicle. The method includes: obtaining a current gear position of the vehicle, a current electric charge level of a power battery and a slope of a road on which the vehicle is driving; determining whether the vehicle is within a taxiing start-stop interval according to the current gear position, the current electric charge level, and the slope; if the vehicle is within the taxiing start-stop interval, obtaining a current speed of the vehicle; if the current speed is greater than or equal to a first speed threshold, and less than a second speed threshold, causing the vehicle to enter a small load stop mode; and if the current speed is greater than or equal to the second speed threshold, and less than a third speed threshold, causing the vehicle to enter a small load stall mode.