Translational motion of an oscillating bubble cluster under sound irradiation is studied experimentally and is modeled in the framework of the classical approach of Bjerknes. An experimental technique is proposed to observe bubble cluster formation and its translational dynamics interacting with wall boundaries due to the secondary Bjerknes force. The translational motion observed in the experiment is modeled by extending the classical theory of Bjerknes on a single bubble; a bubble cluster is treated as a single bubble. The extended Bjerknes theory is shown to allow us to predict the overall trajectory of the cluster translating toward a wall of finite acoustic impedance by tuning acoustic energy loss at the wall. The drag force turns out to be unimportant for the translation of a millimeter-sized cluster that we observed.