A composite semipermeable membrane, which comprises a separating functional layer comprising a reactant of polyfunctional amine with polyfunctional acid halide, wherein a water-soluble organic material is in contact with the separating functional layer, and the separating functional layer has a boron removal ratio of 95% or more, when seawater at 25.degree. C. having a pH of 6.5, a boron concentration of 5 ppm and a TDS concentration of 3.5% by weight is permeated under an operation pressure of 5.5 MPa.