Taking the heteromorphic ellipse and the ellipse as basic figures, this paper defines three independent parameters, i.e. the half-length, half-width, and half-height to establish conditions and definition intervals for five new types of heteromorphic ellipsoid surfaces. The equations of types Ⅲ–Ⅶ heteromorphic ellipsoid surfaces are established through the analytic geometrical method. The geometric characteristics of the five types of heteromorphic ellipsoid surfaces are as follows: the cross-sections on the parallel plane yOz form a heteromorphic ellipse, the contours in the top view form an ellipse or a heteromorphic ellipse, and curves of the profile on the coordinate plane xOz form an ellipse, a semi-heteromorphic ellipse, or a semi-ellipse. The analysis showed that types Ⅲ, Ⅴ, and Ⅶ heteromorphic ellipsoid surfaces have double-symmetry planes, while types Ⅳ and type Ⅵ have single-symmetry planes. The contours of the top view of types Ⅵ and Ⅶ of the heteromorphic ellipsoid surfaces coincides with the xOy profile. The volumes of parts above the contours in the top views of types Ⅲ–Ⅶ heteromorphic ellipsoids accounted for 60.83% of their respective total volumes. These new types of heteromorphic ellipsoid surfaces can be used broad application prospects in the design of special construction projects, floating bodies and landscape modeling.