Abstract: This paper presents the control mesh representation of planar lines of curvature minimal surface using the qusi-Bézier basis and qusi-B-spline basis.The planar lines of curvature minimal surface contains the catenoid and Enneper surface as its special examples.We also implement the dynamic deformation from the catenoid to the Enneper surface.This work provides a powerful tool for introducing the minimal surface into the CAGD/CAD modeling systems.Furthermore,the result also provides a powerful tool for modeling the minimal surfaces by de-Casteljau-like algorithm.