A composite reverse osmosis membrane has a polyamide type skin layer whose specific surface area ranges from 3 to 1000. The composite reverse osmosis membrane of this invention is superior in the salt rejection property and water permeability. The composite reverse osmosis membrane comprises a negatively-charged crosslinked polyamide type skin layer obtained by reacting a compound having polyfunctional amino groups and a polyfunctional acid halide compound having polyfunctional acid halide groups, and a microporous support to support the skin layer. The specific surface area of the skin layer is at least 3. A first stage of reverse osmosis treatment is carried out in a membrane module using this composite reverse osmosis membrane. The skin layer can be coated with a layer of an organic polymer having positively-charged groups e.g. polyethyleneimine in order to be used as another membrane module. The organic polymer of this case is crosslinked, for example, by glutaraldehyde. The layer which is crosslink-coated on its surface area is a composite reverse osmosis membrane excellent in desalination of mineral salt in a low-concentration region and removal of cationic organic materials.