A control device for a vehicle that transmits driving force from an internal combustion engine to a drive wheel via a transmission having a torque converter, characterized by comprising: an accelerator operation amount detecting unit that detects an accelerator operation amount; an engine rotation speed detecting unit that detects an engine rotation speed of the internal combustion engine; a vehicle speed detecting unit that detects a vehicle speed of the vehicle; an input shaft rotation speed detecting unit that detects an input shaft rotation speed of the transmission; an inclination angle detecting unit that detects an inclination angle of a road surface; an engine rotation speed increasing unit that increases the engine rotation speed of the internal combustion engine; an engine stall occurrence predicting unit that predicts occurrence of an engine stall in the internal combustion engine; and a prevention control unit that executes engine stall occurrence prevention control when the engine stall occurrence predicting unit has predicted occurrence of an engine stall, wherein the engine rotation speed increasing unit increases the engine rotation speed on the basis of the input shaft rotation speed detected by the input shaft rotation speed detecting unit on the condition that the accelerator operation amount that indicates that an accelerator pedal is released has been detected by the accelerator operation amount detecting unit, a fact that the vehicle is located on an inclined road surface has been detected by the inclination angle detecting unit and a travel of the vehicle in a direction opposite to a direction in which the vehicle travels by the transmitted driving force has been detected by the vehicle speed detecting unit, and the engine stall occurrence predicting unit predicts occurrence of an engine stall on the basis of a rotation speed difference between the engine rotation speed increased by the engine rotation speed increasing unit and the detected input shaft rotation speed. an accelerator operation amount detecting unit that detects an accelerator operation amount; an engine rotation speed detecting unit that detects an engine rotation speed of the internal combustion engine; a vehicle speed detecting unit that detects a vehicle speed of the vehicle; an input shaft rotation speed detecting unit that detects an input shaft rotation speed of the transmission; an inclination angle detecting unit that detects an inclination angle of a road surface; an engine rotation speed increasing unit that increases the engine rotation speed of the internal combustion engine; an engine stall occurrence predicting unit that predicts occurrence of an engine stall in the internal combustion engine; and a prevention control unit that executes engine stall occurrence prevention control when the engine stall occurrence predicting unit has predicted occurrence of an engine stall, wherein the engine rotation speed increasing unit increases the engine rotation speed on the basis of the input shaft rotation speed detected by the input shaft rotation speed detecting unit on the condition that the accelerator operation amount that indicates that an accelerator pedal is released has been detected by the accelerator operation amount detecting unit, a fact that the vehicle is located on an inclined road surface has been detected by the inclination angle detecting unit and a travel of the vehicle in a direction opposite to a direction in which the vehicle travels by the transmitted driving force has been detected by the vehicle speed detecting unit, and the engine stall occurrence predicting unit predicts occurrence of an engine stall on the basis of a rotation speed difference between the engine rotation speed increased by the engine rotation speed increasing unit and the detected input shaft rotation speed.