Minimal surface is a kind of special surface in differential geometry with important applications in geometric design. In this paper, we propose a new class of parametric polynomial minimal surfaces with arbitrary degree from the viewpoint of geometric modeling. The proposed minimal surface has explicit parametric form, and some interesting geometric properties such as symmetry, containing straight lines and self-intersections. From the geometric properties, the proposed minimal surface can be classified into four categories with respect to $n=4k+1$, $n=4k+2$, $n=4k+3$ and $n=4k+4$, where $n$ is the degree of minimal surface and $k$ is a positive integral number. The explicit parametric form of corresponding conjugate minimal surfaces is given and the isometric deformation is also implemented.