A mode-coupling expression for the shear viscosity coefficient of dense molecular liquids based on the interaction site model is presented. It is a natural extension of the corresponding theory for simple liquids, in which the shear stress auto correlation function is described as the linear combination of the bilinear products of the site-site dynamic structure factor. The theory is applied to water at the ambient condition. The agreement between the theory and the computer experiment is fairly good for the simplicity of the theory.