Carbon capture and storage is one strategy to reduce greenhouse gas emissions. One approach to storing the captured CO2 is to inject it into deep saline aquifers. However, dynamics of the injected CO2 plume is uncertain and the potential for leakage back to the atmosphere must be assessed. Thus, accurate and timely forecasts of CO2 storage via real-time measurements integration becomes very crucial. This study proposes a learning-based, inverse-free prediction method that can accurately and rapidly forecast CO2 movement and distribution with uncertainty quantification based on limited simulation and observation data. The machine learning techniques include dimension reduction, multivariate data analysis, and Bayesian learning. The outcome is expected to provide CO2 storage site operators with an effective tool for real-time decision making.