The energy-momentum tensor of gravitational field is a very important physical quantity. A great debate about the definition of this quantity and the conservation laws occured between Einstein and Levi-Civita et al. eighty years ago. Although the viewpoints of Einstein have occupied a dominant position after this debate, but, for lack of covariance, the gravitational energy-momentum tensor remains one old, great and difficult problem which has not been solved satisfactorily till now. In this paper, the contents of debate and the viewpoints of both sides are presented in detail;a new evaluation for the debate is given;and some results of our new study are introduced;the conclusion that gravitational wave does not transmit energy and its possible experimental test is discussed in particular.