A speed ratio control device for an automatic transmission of a vehicle calculate a minimum engine rotation speed based on a travel load, and sets a target speed ratio such that the engine rotation speed does not fall below the minimum engine rotation speed. If the travel load of the vehicle is equal to or greater than a predetermined value, a higher value is used for the minimum engine rotation speed compared to a case when the travel load of the vehicle is smaller than the predetermined value. Re-acceleration performance of the vehicle under a high travel load as in a case when the vehicle travels uphill while towing another vehicle is thereby improved.