A new hybrid wave model for the prediction of the kinematics and wave evolution of unidirectional irregular wave trains is presented. The model considers the effects of the interaction between the wave components of an irregular wave train up to the second order of wave steepness. Since the majority of measurements are related to the resultant wave properties at fixed points, such as wave elevations, special efforts are made to develop a numerical scheme based on the hybrid wave model to decompose an irregular wave train into its free-wave components given its resultant wave elevation at a fixed point. The numerical scheme has been extensively examined using various wave spectra and is found to be convergent and accurate. The application of the hybrid wave model to the prediction of irregular wave kinematics and wave evolution are demonstrated by comparison with two sets of laboratory measurements and other prediction methods, which is presented in part II of this study. Copyright © 1996 Elsevier Science Ltd.