This control device for an internal combustion engine includes a variable intake valve device and a variable exhaust valve device; and it performs fuel cut-off for a plurality of cylinders of the internal combustion engine. And it further includes: an intake valve control means which, when the fuel cut-off execution condition has come into effect, controls the variable intake valve device, so as to keep in a closed state the intake valve of a cylinder, for which an exhaust valve is not kept in a closed state; and an exhaust valve control means which, when the fuel cut-off execution condition has come into effect, controls the variable exhaust valve device, so as to keep in an open state an exhaust valve of at least a pair of cylinders, between which gases in the pair of cylinders come and go via an exhaust passage as the pistons operate.