Ocean mesoscale eddies are ubiquitous in world ocean and account for 90% oceanic kinetic energy, which dominate the upper ocean flow field. Accurately predicting the variation of ocean mesoscale eddies is the key to understand the oceanic flow field and circulation system. In this article, we propose to make an initial attempt to explore spatio-temporal predictability of mesoscale eddies, employing deep learning architecture, which primarily establishes Memory In Memory (MIM) for sea level anomaly (SLA) prediction, combined with the existing mesoscale eddy detection. Oriented to the western Pacific ocean (125°−137.5°E and 15°−27.5°N), we quantitatively investigate the historic daily SLA variability at a 0.25° spatial resolution from 2000 to 2018, derived by satellite altimetry. We develop the enhanced MIM prediction strategies, equipped with Gated Recurrent Unit (GRU) and spatial attention module, in a scheduled sampling manner, which overcomes the gradient vanishing and complements to strengthen spatio-temporal features for long-term dependencies. At the early stage, the real value SLA input guides the model training process for initialization, while the scheduled sampling intentionally feeds the newly predicted value, to resolve the distribution inconsistency of inference. It has been demonstrated in our experiment results that our proposed prediction scheme outperformed the state-of-art approaches for SLA time series, with MAPE, RMSE of the 14-day prediction duration, respectively, 5.1%, 0.023 m on average, even up to 4.6%, 0.018 m for the effective sub-regions, compared to 19.8%, 0.086 m in ConvLSTM and 8.3%, 0.040 m in original MIM, which greatly facilitated the mesoscale eddy prediction. This proposed scheme will be beneficial to understand of the underlying dynamical mechanism behind the predictability of mesoscale eddies in the future, and help the deployment of ARGO, glider, AUV and other observational platforms.