Abstract: It is a new method to lap the paraboloid parts with fixed abrasive. According to the mechanical analysis of paraboloid under stress, the stress state of paraboloid lapping and the change of relative lapping speed were summarized, and the distribution law of the pellets on the lapping disc was deduced based on the theory of conformal wear of lapping tools summarized by Preston equation. According to the calculation example, the lapping system is designed to meet the requirements. The lapping experiment shows that the maximum error of the surface shape is 0.085 7 mm, and the precision of the surface shape can meet the precision requirements of most parts.