<p>A valve-timing control apparatus of an internal combustion engine (1) provides a valve timing controller (12) capable of continuously and variably controlling the overlap period of an intake valve (16) and an exhaust valve (11) of an internal combustion engine (1). A driving-state determination mechanism determines the driving state of the internal combustion engine (1) and an overlap-period setting apparatus sets the overlap period with the valve timing controller (12). The overlap-period is set during the start of the internal combustion engine (1) on the basis of the determinations of the driving-state determination mechanism which vary as the internal combustion engine starts.</p>