A transmission control device includes a converter that converts continuous accelerator positions detected by an accelerator pedal sensor into a stepped step position, and a controller that controls the gear ratio of a continuously variable transmission based on the converted step position. The converter creates a hysteresis regarding the converted step position, when the accelerator depression amount increases, and when the accelerator depression amount decreases. In the case where the step position reaches a predetermined position or greater, the controller executes kick-down control where the gear ratio is controlled to a low side.