A semipermeable composite membrane comprising a thin semipermeable film of a polymeric material deposited on one side of a microporous substrate, said polymeric material being prepared by crosslinking a soluble polymer containing at least 30 mole % of a recurring unit of the formula ##STR1## wherein all symbols are as defined in claim 1, and having at least 0.2 milliequivalent, per gram of said polymer, of an amino group containing 1 or 2 active hydrogen atoms, with a polyfunctional compound containing at least two functional groups capable of reacting with the amino group having 1 or 2 active hydrogen atoms; and a process for preparing the same. The semipermeable composite membrane of this invention is especially useful for desalination of saline or brackish water by reverse osmosis.