The use of machine learning (ML) in the study of CO2 storage is a hot topic, but the feasibility of applying ML to complex reservoir conditions, such as those with CO2 enhanced shale gas recovery (CO2-ESGR), remains untested. This research aims to develop a novel multi-task ML workflow using simulation data to provide an effective and timesaving approach for the evaluation of CO2 storage and enhanced gas recovery during CO2-ESGR. A three-stage reservoir model, including primary recovery, CO2-ESGR, and CO2 storage, using the Barnett Shale formation as the basis of research was developed to determine the sensitivities of various parameters and provide the data for subsequent ML modeling. A composite ML model, which consists of a combination of Artificial Neural Network (ANN) and Long Short-term Memory (LSTM) algorithms, was used to provide better forecasting performance. The two parts of this ML model include the prediction of gas production during CO2-ESGR and CO2 storage during the CO2 storage stage; its other functionalities include a switching criterion and prediction of CO2 storage during CO2-ESGR. These two parts were optimized by tuning the algorithm hyperparameters and further combined into one model to validate the simulation results. The results show that both gas recovery during CO2-ESGR and CO2 storage during the CO2 storage stage were mainly affected by seven key features, which include matrix porosity, fracture porosity, pressure gradient, geothermal gradient, hydraulic fracture conductivity, and adsorption properties of CO2 and CH4. By applying the ML model, the results on gas recovery during CO2-ESGR were matched with simulation results with an accuracy of 99.9986% for CH4 production and an accuracy of 99.995% for CO2 production. Additionally, the monthly CO2 storage during the CO2 storage process achieved a match to the simulation results with an accuracy of 99.7%. Furthermore, the ML model was economized 99.9% on computational efficiency compared to reservoir simulations. The greatest advantage of this novel ML model is that it can accurately predict production and storage in both CO2-ESGR and CO2 storage without the need of historical production data.