Deep learning inversion has recently drawn attention in geological carbon storage research due to its potential of imaging and monitoring carbon storage in real time, significantly improving efficiency and safety of carbon storage operations. We present a deep-learning full waveform inversion method that after the neural network has been trained can image CO2 saturation and its uncertainty in real time. Our deep learning inversion method is based on the U-Net architecture with the neural network trained on pairs of synthetic seismic data and CO2 saturation models. Accordingly, our training establishes a mapping relationship between seismic data and CO2 saturation models and once fully trained directly estimates CO2 saturation as a function of subsurface location. We further quantify uncertainties of CO2 saturation estimates using the Monte Carlo dropout method and a bootstrap aggregating method. For this proof-ofconcept study, the CO2 training models and data are derived from the Kimberlina 1.2 model, a hypothetical 3D geological carbon storage model that is constructed based on various geological and hydrological data from the Southern San Joaquin Basin, California. We perform deep-learning inversion experiments using noise-free and noisy training and test data sets and compare the results. Our modeling experiments show that 1) the deep-learning inversion can estimate 2D distributions of CO2 fairly well even in the presence of Gaussian random noise and 2) both CO2 saturation imaging and uncertainty quantification can be done in real time. Our results suggest that the deep-learning inversion method can serve as a robust real-time monitoring tool for geological carbon storage and/or other time varying reservoir/aquifer properties that result from injection, extraction, and/or other subsurface transport phenomena.