Abstract: For the dynamical equation system(a three-dimensional autonomous system) of hemoglobin, given in [1],we make the following qualitative investigation:(1)pointing out that, all meaningful solutions should be in a tetrahedroid. and -that,its..four surfaces are without contact;(2)finding all singular points, and proving that only two, of them are respectively situayed on a pair of seperate edges,and that other singular points are outside the tetrahedroid and meaningless;(3)proving that, among seven physical parameters of this system, only the sign of parameter b determines the properties of these two singular points;(4)clearing up the relation between this system and MWC model^[3]. The investigation shows that this system reflects the dynamical properties of hemoglobin satisfacto rily.