Abstract: The Hermite model has been widely used in estimating the short term extrema of non-Gaussian processes since late 1980s. When the non-Gaussianity of a process is very strong, especially with a large skewness, the commonly used cubic Hermite model has its limited capacity to capture the characteristics of the tail distribution of the extreme value. However, higher-order models are not recommended for engineering use due to the uncertainty in moments. In this paper, a hybrid use of ordinary central moments (C-moments) and linear moments (L-moments) is proposed to construct Hermite models up to quartic order. A lognormal function is chosen as the original nonlinear system for validating the performance of hybrid Hermite models. Both analytical solutions and numerical solutions using Monte-Carlo simulations are investigated. The comparative study involves the conventional Gumbel method and the averaged conditional exceedance rate (ACER) method. The results show that the proposed hybrid Hermite models render better accuracy and higher robustness in estimating the extreme value.