We investigate the nonlinear Landau-Zener tunnelling of Bose-Einstein condensate (BEC) in an accelerating optical lattice with two- and three-body interactions between the particles. The influence of the three-body interaction on the eigenstates and the transition probability are discussed both analytically and numerically.The analytical eigenstates and the tunnelling probability are obtained,which are verified by numerical methods.It is shown that the eigenstates and the tunnelling probability are modified dramatically by three-body interaction.