A scalable on-chip single-photon source at telecommunications wavelengths is an essential component of quantum communication networks. In this work, we numerically construct a pulse-regulated single-photon source based on an optical parametric amplifier in a nanocavity. Under the condition of pulsed excitation, we study the photon statistics of the source using the Monte Carlo wave-function method. The results show that there exists an optimum excitation pulse width for generating high-purity single photons, while the source brightness increases monotonically with increasing excitation pulse width. More importantly, our system can be operated resonantly, and we show that in this case the oscillations in g(2)(0) are completely suppressed.