An apparatus for controlling a vehicle includes an engine including at least one combustion chamber configured to generate power for driving the vehicle by combustion of fuel, a torque converter including an impeller, a turbine, and a damper clutch and configured to convert torque output from the engine through an operation fluid, a continuously variable transmission including a driving pulley, a driven pulley, and a belt, a forward clutch configured to selectively block power delivery between the torque converter and the continuously variable transmission, and a controller configured to perform a slip control of the forward clutch while the vehicle is coasting, re-inject fuel into the combustion chamber of the engine when a fuel re-injection condition is satisfied, release engagement of the damper clutch after performing a slip control of the damper clutch of the torque converter, and fully engage the forward clutch.