Abstract: Cell-to-cell mapping method is a powerful tool for globally analyzing into nonlinear system. Byint roducing the cell-to-cell mapping method, the predictability of climate in a most simplified air-sea coupled model is studied in this paper. It is indicated that there exists a maximum predictability limit in climate prediction. For the prediction beyond the daily predictability limit, it is proved by using simple cell-to-cell mapping idea that mean value is predictable, and the quantitative resultis obtained. The study also shows that both coupling mechanism and improvement of observational error prolongs the maximum predictability limit.