Abstract: In quantum tunneling a particle with energy E can pass through a high potential barrier V(>E) due to the wave character of the particle. Bose-Einstein condensates can display very strong tunneling depending on the structure of the trap, which may be a double-well or optical lattices. We employed for the first time to our knowledge the periodic instanton method to investigate tunneling of Bose-Einstein condensates in optical lattices. Our results show that there are two kinds of tunneling in this system, Landau-Zener tunneling between extended states of the system and Wannier-Stark tunneling between localized states of the system, and that the latter is 1000 times faster than the former. We also obtain the total decay rate for a wide range of temperature, including classical thermal activation, thermally assisted tunneling and quantum tunneling. Our results agree with experimental data in references［1, 2］.Finally, we propose an experimental protocol to observe this new phenomenon in future experiments.