A curved surface machining method for machining a curved surface through unidirectional cutting by automatically creating a pick-feed path that will not cause a tool (TL) to strike a workpiece when a pick-feed is performed, pick-feeding the tool along the path, and thereafter performing cutting. The pick-feed path is obtained by using a given tool retraction quantity l for retracting the tool from a cutting path end point Pe, a clearance plane (CPL), coordinate values of the cutting end point Pe, and coordinate values of a cutting starting point Ps on the next cutting path. Specifically, there are obtained: coordinate values of a point Pa distanced from the cutting path end point Pe by the tool retraction quantity l in the direction of the central axis of the tool; coordinate values of the foot Pb of a perpendicular dropped from the point Pa to the clearance plane (CPL); coordinate values of a point Pd distanced from the cutting starting point Ps of the next cutting path (PT2) by the tool retraction quantity l in the direction of the central axis of the tool; and coordinate values of the foot Pc of a perpendicular dropped from the point Pd to the clearance plane. The path Pe.fwdarw.Pa.fwdarw.Pb.fwdarw.Pc.fwdarw.Pd.fwdarw.Ps serves as the pick-feed path.