Abstract: The influence of the eccentric vibration amplitude of spindle and the grinding parameters on the surface waviness is investigated according to the cross-grinding method for large-diameter aspheric mirrors, and a three dimensional (3D) model of the mechanism of grinding surface waviness is established. The relationship between grinding surface 3D waviness and machining process parameters is analyzed by simulation experiments, and the optimal range of grinding process parameters is proposed for the specific spindle. The grinding experiment results show that the relationship between the established 3D waviness model and grinding process parameters is reasonable. The wheel speed of 1600 to 1 800 r/min , the X axis feed velocity of 1 to 3 mm/r and the workpiece speed of 20 r/min are optimal technological parameters.