A method for calculating the nuclear magnetic shielding constant of atoms in solution is proposed based on the ab initio electronic structure theory combined with the extended reference interaction site model in statistical mechanics for molecular liquids. The method is applied to a water molecule solvated in water, acetone, chloroform, and carbon tetrachloride. The results for solvation effect demonstrate capability to predict the experimental results. The theory provides a tool to investigate the solvent effect on the nuclear magnetic shielding and its temperature dependence from a molecular viewpoint. The theory takes account for the effect of the electrostatic interaction on the electronic structure of solute, but disregards the electron overlap. The effect of intermolecular overlap of the electron on the nuclear magnetic shieldings is examined using a molecular cluster model.