The levitation force characteristics in a superconducting levitation device are determined not only by the geometry and electromagnetic properties of its components, but also by the initial cooling process of the superconductor. In this paper we present the experimental results of effects of the different initial cooling heights between a superconductor and magnet on the levitation force characteristics including maximum levitation force, relaxation of the levitation force and drift of the levitation force caused by the magnet vibration. It was found that the different cooling heights have large influences on the levitation force characteristics of YBCO bulk.