Geologic CO2 sequestration (GCS) has been considered a viable engineering measure to decrease global CO2 emissions. The real-time monitoring to detect possible CO2 leakage is an important part of big-scale GCS deployment. In this work, we introduce a deep-learning-based algorithm using a hybrid neural network for detecting CO2 leakage based on bottom-hole pressure measurements. The proposed workflow includes the generation of train-validation samples, the coupling process of training-validating, and the model evaluation. This work solves the diffusivity equation for pressure within a simulation framework, used to generate datasets under no-leakage conditions. A Bayesian optimization process is performed to optimize the model hyperparameters. We test the performance of the hybrid neural network, referred to as Convolutional Neural Network (CNN) and Bi-directional Long Short-Term Memory (CNN-BiLSTM) on the bottom-hole pressure data collected from CO2 leakage simulations. Results show that the CNN-BiLSTM model can successfully detect CO2 leakage events by comparing the difference between the predicted (no leakage) and tested bottom-hole pressures. We further compare its superiority with Convolutional Neural Network (CNN), Long Short-term Memory (LSTM), Bidirectional Long Short-term Memory (BiLSTM), and CNN-LSTM. Our proposed model achieves the highest accuracy with the same datasets. The CNN-BiLSTM outperforms other models owing to 1) its capacity to process image-based input, which could accurately capture input formation, especially in cases with highly heterogeneous permeability; 2) its bidirectional ability to capture time-series dependency. Other models, like LSTM and BiLSTM, take value-based input, which is insufficient to describe the input information in highly heterogeneous cases. In contrast, the CNN model suffers from capturing the temporal dependency features. This approach provides an efficient and practical CO2 leakage detection method and can be implemented in large-scale GCS for real-time monitoring applications.