Ship parametric roll is one of the main reasons for marine accidents and is introduced into the second-generation intact stability criteria by the International Maritime Organization (IMO) recently. In this paper, a 6-DOF three-dimensional time-domain model based on the IRF (Impulse Response Function) method is constructed to predict large-amplitude ship motions and investigate the phenomenon of parametric roll in head waves as well as major factors. The F-K forces and the restoring forces are calculated on the instantaneous wet surface while the radiation and diffraction forces are kept linear and transformed from frequency-domain results calculated with the three-dimensional Havelock form translating-pulsating source green function method. The proposed weakly nonlinear time-domain model is used to simulate motions of the C11 containership, which predicts the occurrence of the parametric roll successfully and shows a good agreement with the experimental data in amplitude. The inner mechanism of parametric roll is revealed by investigating the time-history and resonance frequencies of restoring forces and coefficients numerically.