Disclosed is an apparatus and method for operating vehicular accessories during an engine stop using a one-way clutch pulley, the apparatus including the one-way clutch pulley configured to drive the vehicular accessories, and including a coupler and a one-way clutch. The one-way clutch pulley includes an engine crank shaft configured to connect to an engine of a vehicle; the coupler configured to couple with the engine crank shaft; the one-way clutch configured to couple with the coupler; and a pulley configured to connect to the one-way clutch, and the one-way clutch is configured to connect to the pulley and to rotate in one direction.