Greenwood and Williamson (GW) and Greenwood and Tripp (GT) elastic contact models have extensively been used previously for the mixed-lubrication analysis of water-lubricated journal bearings (WLJBs). The approximate expressions of a parabolic cylinder function involved in these contact models are available in the literature which makes these models easy to implement in the mixed-lubrication analysis. However, approximate expressions available so far are valid only for the Gaussian distribution of asperity heights. Moreover, elastic-plastic contact models with few exceptions have rarely been used in the mixed-lubrication analysis of WLJBs. The present work demonstrates a simple numerical procedure to predict the mixed-lubrication parameters for WLJBs. The average Reynolds equation considering non-Gaussian flow factors is solved along with film thickness and load balance equations in a coupled manner. A routine is developed to predict the pressure curve (a plot between average asperity pressure and rigid body displacement) for different contact models and non-Gaussian surface topography, and the asperity pressure for a particular surface topography is predicted utilizing the concept of a macro-micro approach. The effect of non-Gaussian surface topography on the tribological performance of WLJBs is discussed in detail. The influence of different contact models on the performance of WLJBs is also presented. It is shown that the GT elastic contact model fails to simulate the effect of kurtosis and skewness properly. However, the Kogut and Etsion (KE) elastic-plastic contact model which is based on finite element method (FEM)-based analysis excellently simulates the non-Gaussian effect on the performance of the WLJB.