A new method is developed for calculating hydration free energies (HFEs) of polyatomic solutes. The solute insertion is decomposed into the creation of a cavity in water matching the geometric characteristics of the solute at the atomic level (process 1) and the incorporation of solute-water van der Waals and electrostatic interactions (process 2). The angle-dependent integral equation theory combined with our morphometric approach and the three-dimensional interaction site model theory are applied to processes 1 and 2, respectively. Neither a stage of training nor parameterization is necessitated. For solutes with various sizes including proteins, the HFEs calculated by the new method are compared to those obtained using a molecular dynamics simulation based on solution theory in energy representation (the ER method developed by Matubayasi and co-workers), currently the most reliable tool. The agreement is very good especially for proteins. The new method is characterized by the following: The calculation can rapidly be finished; a solute possessing a significantly large total charge can be handled without difficulty; and since it yields not only the HFE but also its many physically insightful energetic and entropic components, it is best suited to the elucidation of mechanisms of diverse phenomena such as the receptor-ligand binding, different types of molecular recognition, and protein folding, denaturation, and association.