In carbon capture and sequestration, developing effective monitoring methods is needed to detect and respond to CO2 leakage. CO2 leakage detection methods rely on geophysical observations and monitoring sensor network. However, traditional methods usually require the development of site-specific physical models and expert interpretation, and the effectiveness of these methods can be limited to different application locations, operational scenarios, and conditions. In this paper, we developed a novel data-driven leakage detection method based on densely connected convolutional neural networks. Our method differs from conventional leakage monitoring methods by directly learning a mapping relationship between seismic data and the CO2 leakage mass. To account for the spatial and temporal characteristics of seismic data, our novel networks architecture combines 1D and 2D convolutional neural networks. To overcome the computational expense of solving optimization problems, we apply a densely-connecting strategy in our network architecture that reduces the number of network parameters. Based on the features generated by our convolutional neural networks, we further incorporate a long short-term memory network to utilize time-sequential information, which further improves the detection accuracy. Finally, we employ our detection method to synthetic seismic datasets generated based on flow simulations of a hypothetical CO2 storage scenario with injection into a partially compartmentalized sandstone storage reservoir. To evaluate method performance, we conducted multiple experiments including a random leakage test, a sequential test, and a robustness test. Numerical results show that our CO2 leakage detection method successfully detects the leakage and accurately predicts the leakage mass, suggesting that it has the potential for application in monitoring of real CO2 storage sites.