Abstract: In order to further expand roots pump potential performance and improve the rotor-contour construction method based on the current top-axis, two new methods of contour construction based on the median-axis are proposed; with the application of parabolic contour as an example, from the contacting-line and transmission-angle on either conjugate point as constructing parameters, the abscissa of the conjugate point is the construction variable, the inter-construction equations for the lobe contour are derived firstly; from the minimum curvature radius on lobe contour being zero, the minimum parabolic coefficient and following maximum shape coefficient are derived secondly; the lobe cross section natures and following potential performances under three different construction methods of outer median-axis and inner median-axis and outer top-axis are compared and analyzed finally. The results show that the functional analysis of constructing parameters determines the complexity of the contour construction, and the abscissa of the parabolic contour point as the construction variable can simplify the complexity. The maximum shape coefficient is determined by the minimum parabolic coefficient, and the minimum parabolic coefficient is determined by the zero minimum curvature radius on the pending contour. For the three different construction methods of outer median-axis and inner median-axis and outer top-axis, the minimum parabolic coefficient is 19.52/0/0.60 under two lobes, 1.81/0/0.42 under three lobes, 0.75/0/0.31 under four lobes; the maximum shape coefficient is 1.32/1.71/1.49 under two lobes, 1.24/1.50/1.39 under three lobes, 1.08/1.38/1.32 under four lobes; the concave function features of the outer working contour are easier to be realized by the inner and outer median-axis construction method than the top-axis construction method, and the lobe cross-sectional area inertia moment is decreased by 9.77% and 12%, etc. It is concluded that the construction method based on the median-axis can better reduce the conjugate leakage and improve the rotational stability than the current top-axis construction method.