We present a solution to the problem of reflection and refraction of a polarized Gaussian beam at the interface between the transparent medium and the moving object based on Minkowski’s constitutive relations. The Goos–Hänchen (GH) and Imbert–Fedorov (IF) effects are discussed in detail when the object moves parallel to the interface. It is shown that the IF shifts of reflection and transmission beams can reach several wavelengths of the incident beam at some certain incident angles and moving velocities of the object. The transitions from the positive IF shift to the negative IF shift have been observed with the increase of the velocity of the moving object. Furthermore, our calculations show that some unusual GH effects can also be caused by the movement of the medium. The physical origins for these phenomena have been analyzed. It is well known that the IF shift is directly related to the spin-Hall effects of light. Thus, these findings can also provide an alternative pathway for controlling the spin-Hall effects of light.