Mercury injection capillary pressure analysis is a methodology for determining different petrophysical properties, including bulk density, porosity, and pore throat distribution. In this work, distinct parameters derived from mercury injection capillary pressure tests was considered for the prediction of permeability by coupling machine learning and theoretical approaches in a dataset composed of 246 tight sandstone samples. After quality checking the dataset, the feature selection was carried out by correlation analysis of different theoretical permeability models and statistical parameters with the measured permeability. Finally, porosity, median capillary pressure, Winland model, and mean pore-throat radius (corresponding to the saturation range 0.4-0.8) were chosen as the input features of the machine learning model. As the machine learning approach, a support vector machine (SVM) model with a radial basis function kernel was proposed. Furthermore, the model and its metaparameters were trained with a particle swarm optimization (PSO) algorithm to avoid over-fitting or under-fitting. In contradiction to the theoretical models, the implemented SVM-PSO model could acceptably predict the experimentally measured permeability values with an R ${}^2$ rate of over 0.88 for training and testing datasets. The introduced approach could reduce the mean relative errors from about 10 to values less than 0.45. The improvements were more significant for low permeability samples. This successful implementation shows the potential of coupled usage of theoretical and machine learning methodologies for improved prediction of permeability of tight sandstone rocks.