It is an object of the present invention to provide a process for producing, easily and at a low cost, a composite semipermeable membrane having excellent contamination resistance, especially microbial contamination resistance, and a composite semipermeable membrane produced by the process. The process for producing a composite semipermeable membrane of the present invention comprises forming a skin layer including a polyamide resin obtained by a reaction between a polyfunctional amine component and a polyfunctional acid halide component on the surface of a porous support; forming a polymer layer (A) including a silver salt compound on the skin layer directly or through other layers; and reducing the silver salt compound to precipitate metal silver in the polymer layer (A) and/or on the surface thereof.