A number of techniques to track rainfall patterns by use of radar observations have been developed over the years. We present a method for radar-echo tracking based on Hu invariant moments. The method has been tried on several sequences of test images, and the derived displacement fields were in good agreement with the real motions of the tested objects. For the real data obtained from the conventional meteorological radar in Legionowo the method occasionally failed when changes in the radar echo between observations were too large.