In order to study Gaussian beam propagation in the spherical refractive surfaces，the relationship between the location and radius of the object beam waist and ones of the image beam waist are deduced theoretically by using the paraxial ray tracing in geometrical optics. By hypothesis that Gaussian beam ray is the rectilinear generatrices of hyperboloid of one sheet，we simulate the Gaussian beam propagation through lens systems with the ray tracing method. Simulation results show that when the distance between the Gaussian beam waist and the object focus of a lens system is much larger than the confocal parameter of the Gaussian beam，the simulation results for the waist location and the waist radius are consistent with the theoretical results obtained from the paraxial approximation， otherwise，the simulation results will be inconsistent with theoretical results.