A composite semipermeable membrane which satisfies the following relationship 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: Boron removal ratio (%).gtoreq.95-4.times.membrane permeation flow rate (m.sup.3/m.sup.2day).