A multi-stage seawater desalination apparatus comprising: a high-pressure pump that is mounted on a raw water line through which raw water (11 Cl) is supplied, for feeding the raw water (11 Cl) as a high-pressure feed water at a predetermined high pressure; means for adding chlorine (Cl) to the raw water (11 Cl); a high-pressure reverse osmosis device that includes a high-pressure reverse osmosis membrane for concentrating a salt content in the high-pressure feed water fed by the high-pressure pump; a first drain valve that is mounted on a permeated water line through which permeated water (14 Cl) that has passed through the high-pressure reverse osmosis device is supplied downstream, for temporarily draining the permeated water (14 Cl) of an initial start-up; a low-pressure pump that is mounted on a permeated water line provided downstream of the first drain valve, for feeding the permeated water (14 Cl) as a low-pressure feed water at a predetermined low pressure which is lower than the predetermined high pressure; a low-pressure reverse osmosis device that includes a low-pressure reverse osmosis membrane for concentrating a salt content in the low-pressure feed water fed by the low-pressure pump; a second drain valve that is mounted on a discharge line on a concentrated water side of the low-pressure reverse osmosis device, for temporarily discharging the low-pressure feed water of the initial start-up supplied to the low-pressure reverse osmosis device; an oxidation-reduction potential meter for measuring an oxidation-reduction potential of the low-pressure feed water; a first reducing agent supplying unit for supplying a reducing agent that neutralizes chlorine to the raw water line; a second reducing agent supplying unit for supplying the reducing agent to the permeated water line; and a third reducing agent supplying unit for supplying the reducing agent to the low-pressure feed water based on the oxidation-reduction potential measured with the oxidation-reduction potential meter in order to neutralize the chlorine. a high-pressure pump that is mounted on a raw water line through which raw water (11 Cl) is supplied, for feeding the raw water (11 Cl) as a high-pressure feed water at a predetermined high pressure; means for adding chlorine (Cl) to the raw water (11 Cl); a high-pressure reverse osmosis device that includes a high-pressure reverse osmosis membrane for concentrating a salt content in the high-pressure feed water fed by the high-pressure pump; a first drain valve that is mounted on a permeated water line through which permeated water (14 Cl) that has passed through the high-pressure reverse osmosis device is supplied downstream, for temporarily draining the permeated water (14 Cl) of an initial start-up; a low-pressure pump that is mounted on a permeated water line provided downstream of the first drain valve, for feeding the permeated water (14 Cl) as a low-pressure feed water at a predetermined low pressure which is lower than the predetermined high pressure; a low-pressure reverse osmosis device that includes a low-pressure reverse osmosis membrane for concentrating a salt content in the low-pressure feed water fed by the low-pressure pump; a second drain valve that is mounted on a discharge line on a concentrated water side of the low-pressure reverse osmosis device, for temporarily discharging the low-pressure feed water of the initial start-up supplied to the low-pressure reverse osmosis device; an oxidation-reduction potential meter for measuring an oxidation-reduction potential of the low-pressure feed water; a first reducing agent supplying unit for supplying a reducing agent that neutralizes chlorine to the raw water line; a second reducing agent supplying unit for supplying the reducing agent to the permeated water line; and a third reducing agent supplying unit for supplying the reducing agent to the low-pressure feed water based on the oxidation-reduction potential measured with the oxidation-reduction potential meter in order to neutralize the chlorine.