a fuel supply control device for an engine having fuel cutting means for cutting off the supply of fuel to said engine when the engine speed has become greater than or equal to a first predetermined speed during deceleration running in a condition where the throttle angle is less than or equal to a predetermined angle, fuel supplying means for supplying fuel to said engine when the engine speed has become a second predetermined speed less than said first predetermined speed after the fuel cut by said fuel cutting means, and fuel cut engine speed changing means for changing the engine speed at which said fuel cutting means operates to a third predetermined speed greater than said first predetermined speed when said fuel supplying means has been operated;

an automatic transmission having a torque converter with a lock-up clutch;

lock-up preparing means for starting the supply of hydraulic pressure for operating said lock-up clutch of said automatic transmission when the main shaft speed in said automatic transmission has become a fourth predetermined speed greater than said first predetermined speed and less than said third predetermined speed during the fuel supply to said engine in a condition where the throttle angle is less than or equal to said predetermined angle and the fuel cut engine speed has been changed to said third predetermined speed by said fuel cut engine speed changing means;

lock-up determining means for determining that said lock-up clutch has been engaged when the engine speed is equal to the main shaft speed; and

fuel cut engine speed returning means for returning the engine speed at which said fuel cutting means operates from said third predetermined speed to said first predetermined speed when the engagement of said lock-up clutch has been determined by said lock-up determining means.