To manufacture curved surface gratings with highly consistent blazing angles, the curve-fitting motion of the three-dimensional (3D) stage is essential. Therefore, an investigation of the 3D stage was performed based on a control algorithm for the curved blazed grating etching system. First, a concept of the 3D stage of the curved blazed grating etching system was introduced. Subsequently, according to the actual requirement of the etching machine, the theoretical calculating method for the track of the stage was provided. Then, the arc-fitting algorithm of the stage was proposed and the curve-fitting motion of the stage was performed. Finally, the actual motion tracks of the 3D stage were measured and compared with ideal tracks. Experimental results demonstrate that the cumulative positioning error of the linear fitting motion of the stage after 15 cycles is less than 0.218 mm, and the slope angle error is less than 0.02°; the cumulative positioning error of the curve fitting motion of the stage after 40 cycles is less than 0.2 mm and the rotating angle error is in the range of -0.2°-0.1°. This method has realized the function of scanning etching and oscillating etching of the 3D stage. The stability, accuracy, and interference rejection of the stage satisfy the processing requirements.