Numerical approximation of minimal surface is an important problem in the form-finding of structural membranes. In this paper, we present a novel approach to construct minimal surface from a given boundary by quasi-harmonic Bezier approximation. A new energy functional called quasiharmonic energy functional is proposed as the objective function to obtain the quasi-harmonic Bezier surface from given boundaries. The quasi-harmonic mask is also proposed to generate the approximate minimal surfaces by solving a sparse linear system. The efficiency of the proposed methods is illustrated by several modeling examples.