Abstract: Parametric surfaces play an important role in CAD. Aiming at the guided approximation problem under surface constraints and shape preservation, a constrained guided geometry surface approximation algo-rithm is proposed. Firstly, the guided geometry is discretized, and the discrete points are projected onto the target surface to obtain offset vectors. Then, the constraint matrix and the unconstrained matrix containing the shape preservation term are constructed sequentially, which are solved by the least squares method combined with the Lagrange multiplier method to obtain the offset surface of the current iteration. Finally, the original surface and the offset surface are superimposed, and after multiple iterations, the basic surface is driven to fit the guided geometry to the greatest extent while maintaining the original shape. Experi-mental results under various complex constraint conditions show that the algorithm can strictly satisfy constraints with stable convergence and high precision, and the generated surfaces have good morphology, which can provide an effective tool for surface deformation in industrial scenarios such as automotive body design.