In this paper, quintic parametric polynomial minimal surface and their properties are discussed. We first propose the sufficient condition of quintic harmonic polynomial parametric surface being a minimal surface. Then several new models of minimal surfaces with shape parameters are derived from this condition. We also study the properties of new minimal surfaces, such as symmetry, self-intersection on symmetric planes and containing straight lines. Two one-parameter families of isometric minimal surfaces are also constructed by specifying some proper shape parameters.