Based on the narrow-band stochastic processes theory and Hermite transform, this paper proposed a method to study the extreme dynamic response of the parametric roll of ships. Taking the C11 container ship as an example, the average extremum of the stochastic parametric roll of the ship was estimated. A comparison of the results of Monte Carlo simulation indicates that the estimation error is lower than 1%, which proves that the proposed method is valid. Meanwhile, the prediction accuracy of the proposed method in this paper by using 20 time history samples is the same as that of the Monte Carlo method by using 10⁴ time history samples, which proves the efficiency of the proposed method. Then, the conventional Gumbel model was used to estimate the extremum of the C11 parametric roll. A comparison of the results shows that the estimation error of the conventional Gumbel model is quite large, proving that the conventional Gumbel model is not appropriate to estimate the extreme responses of strong non-linear motions, such as the parametric roll of ships. However, even if the proposed method is used to predict extreme values, there is a certain deviation from the model test results. The analysis indicates that this prediction error is caused by ignoring the correlation between the maximum values.