A curved surface machining method that performs finishing of the surface of a workpiece into a curved surface. The method includes the steps of: setting a workpiece in a rotating or stationary state in a water tank filled with an abrasive-containing solution into which an abrasive with a grain size of less than 1 m has been admixed; and spraying a high-speed fluid in the abrasive-containing solution while a position, direction, and angle thereof is controlled relative to the workpiece, thus grinding and finishing the surface of the workpiece to an intended surface roughness and profile accuracy.