To produce a composite semipermeable membrane having a high calcium removal rate, a high TDS removal rate, and a high water permeability.

A composite semipermeable membrane composed of a microporous supporting membrane and a polyamide separation function layer formed thereon and prepared by polycondensing a polyfunctional amine with a polyfunctional acid halide and having a TDS removal rate of 99.5% or higher when measured by allowing seawater having a temperature of 25C, a pH of 6.5, and a TDS concentration of 3.5% to permeate thereinto at an operation pressure of 5.5 MPa is subjected to a treatment of contact with a solution of an organic compound of a urea, thiourea, or guanidine type.