Based on the semiclassical quantum theory, we study the dynamical behaviors of Bose-Einstein condensate in an asymmetric Josephson junction. It is shown that the Josephson effect appears in the system when the ratio χ　of the difference of two ground state energies to the interaction energies is zero. When χ≠0, the dynamical behavior of the system shows both the macroscopic quantum tunneling and the macroscopic quantum localization.