The seasonal Predictability Barrier (PB) of Sea Surface Temperature Anomaly (SSTA) is characterized by a rapid loss of prediction skills at a specific season in dynamic models. To investigate whether this PB phenomenon is caused by the inherent nonlinearity of the air-sea coupled system that leads to chaos under certain conditions, a statistical method - Sample Entropy, was introduced to investigate the spatial-temporal distribution of the chaotic degree of SSTA time series in the tropic Pacific. The results showed that high chaotic values existed in Niño 3 and Niño 3.4 regions in April and May, and in Niño 4 region in May and June, which matched the PB timing previously reported in these regions. Furthermore, the chaotic signal moves westward from March to June longitudinally in the tropical Pacific, leading to a similar linear variation of PB timing along the longitude.