In this paper we made a study of ray propagation and transformation through a conical GRIN rod lens with spherical end surfaces based on the formula of ray refraction on the spherical surfaces and the ray equation. On the basis of the ray transmitting matrix obtained an equivalent optical system of the conical GRIN rod lens with spherical end surfaces is proposed. The formulas for determing the principal planes, focal planes and the focal lengths are derived and the paraxial imaging Gaussian formula is also given. All the results can b? applied to the oylindrioal or radial GRIN rod lens while the tapej: is made zero.