Parametric polynomial representation is a standard form widely used in Computer-Aided Design. In this paper, from the viewpoint of geometric modeling, we study some properties of a class of minimal surface with $n$ degree proposed by Xu in paper \cite{xu2015}. We compute two holomorphic functions which can construct the parametric form in Weierstrass representation of the minimal surface with $n$ degree. Moreover, we give the normal curvature of these surfaces with canonical principal parameters and study some properties of this class of surface.