A reverse osmosis membrane apparatus has a plurality of high pressure vessels 12a and 12b in parallel with each other with respect to introducing passage 18 of clarified seawater obtained by subjecting raw seawater to sterilization and removal of relatively large foreign substances. The high pressure vessels 12a and 12b have first-stage reverse osmosis membrane elements 14a and 14b, respectively. Concentrated seawater subjected to membrane separation in the high pressure vessels 12a and 12b flows into a high pressure vessel 16. In the high pressure vessel 16, a plurality of reverse osmosis membrane elements 42 are arranged in series. When a detected value obtained by a differential pressure meter 56a or 56b provided for the high pressure vessel 12a or 12b exceeds a threshold value, introduction of the clarified seawater is stopped, and the reverse osmosis membrane element is washed or replaced.