The minimal surfaces have been extensively employed in many areas such as architecture, aviation, ship manufacture, and so on. However, the complexity of the minimal surface equation prevents people from modeling the minimal surface in CAD/CAGD. In this paper, based on the nonlinear programming and the FEM (finite element method), the approximation to the solution of the minimal surface equation bounded by Bézier or B-spline curves is investigated. A global method, which is called numerical extension method, is appealed to in the whole iterative process and linearize the nonlinear finite element system by using a simple iteration. Some numerical results are given in this paper.