There is provided a composite semipermeable membrane that shows a high salt removal ratio and high performance in rejecting boron that is not dissociated in the neutral region. The composite semipermeable membrane is produced by a process that includes forming a separating functional polyamide layer on a porous substrate film, while using an organic solvent solution containing a specific cyclic aliphatic compound or a specific aromatic compound such that a polyamide molecule that forms the separating functional polyamide layer has a partial structure composed of "a cyclic aliphatic group or an aromatic group having at least two specific substituents, at least one of which contains a heteroatom bond and a carbonyl group at the .beta. or .gamma. position".