Abstract: First, the necessary and sufficient conditions for the existence of parabolic section of a quadratic surface are given according to the parameter equation of the parabola. Secondly, the necessary and sufficient conditions for the existence of parabolic sections, which are parallel to the coordinate plane and  the z-axis and intersecting with the z-axis, are given respectively with combining the projection equations of the parabola and its invariant. Finally, the existence problem for parabolic sections of five typical quadratic surfaces is discussed.

Key words: quadratic surface, parabola, parabolic section, invariant, equation, existence