The invention concerns a method of and an apparatus for continuously desalinating water by reverse osmosis, in particular desalinating sea water, wherein salt water is introduced under a first pressure by means of a delivery pump into a pressure compensating device, salt water is continuously introduced from the pressure compensating device at a second increased pressure into a membrane module and separated therein by means of a membrane into desalinated water and concentrated salt water, and the concentrated salt water discharged from the membrane module is continuously introduced under approximately the second pressure into the pressure compensating device and used there for acting with approximately the second pressure on the salt water introduced into the pressure compensating device and for introducing the salt water into the membrane module. In order to avoid disturbances in operation and possibly damage to the membrane because of a reduced flow over the membrane surface, it is provided in accordance with the invention that a continuous flow of the salt water introduced into the membrane module is maintained over the surface of the membrane by means of salt water discharged from a reservoir.