A valve-timing control apparatus of an internal combustion engine provides a valve timing controller capable of continuously and variably controlling the overlap period of an intake valve and an exhaust valve of an internal combustion engine. A driving-state determination mechanism determines the driving state of the internal combustion engine and an overlap-period setting apparatus sets the overlap period with the valve timing controller. The overlap-period is set during the start of the internal combustion engine on the basis of the determinations of the driving-state determination mechanism which vary as the internal combustion engine starts.