In the design stage of construction projects, determining the soil permeability coefficient is one of the most important steps in assessing groundwater, infiltration, runoff, and drainage. In this study, various kernel-function-based Gaussian process regression models were developed to estimate the soil permeability coefficient, based on six input parameters such as liquid limit, plastic limit, clay content, void ratio, natural water content, and specific density. In this study, a total of 84 soil samples data reported in the literature from the detailed design-stage investigations of the Da Nang–Quang Ngai national road project in Vietnam were used for developing and validating the models. The models’ performance was evaluated and compared using statistical error indicators such as root mean square error and mean absolute error, as well as the determination coefficient and correlation coefficient. The analysis of performance measures demonstrates that the Gaussian process regression model based on Pearson universal kernel achieved comparatively better and reliable results and, thus, should be encouraged in further research.