Patient-specific computational modeling of cardiac electrophysiology (EP) has been shown to have a potential utility in a wide range of arrhythmia prognostics and treatment applications. Yet, it requires extensive computational resources, posing a critical challenge for expanding its application in the clinic. Hence, there is a pressing need to develop accurate and trustable personalized EP heart models with affordable computational costs. We develop a novel approach to modeling patient-specific cardiac electrophysiology, which utilizes, at a much-reduced cost, deep learning in lieu of solving the equations for electrical wave propagation. The new approach is developed based on an operator-learning neural network (DeepONet) to predict the propagation of electric signals in different patient-specific heart chambers (Fig. a). First, we parametrize the geometry of atria and ventricles from a cohort of patients (300+) with principal component analysis (PCA), which implicitly encodes geometric information such as wall thickness, fiber orientation, or fibrosis of each heart (Fig. b). Next, we perform pacing using the computational approach on each geometry and collect the simulated data as the training dataset of the deep-learning model. Then, we train our model to predict electric signal propagation given the encoded geometric information with the pacing location. After training, the accuracy of the deep learning approach is demonstrated by comparing its predictions with simulation results on unseen geometries: the averaged maximum relative difference is lower than 10%, and the mean relative error is lower than 5%. Regarding time cost, our model makes predictions within a fraction of a second on a personal laptop, whereas a standard computational model takes up to 12+ hours on clusters with multiple CPUs (Fig. c). We propose a novel deep-learning approach for modeling patient-specific cardiac electrophysiology with high accuracy and reduced computational cost. This development paves the way for the utilization of personalized cardiac EP modeling in clinical applications, as part of the clinical workflow, in ablation target predictions, and in arrhythmia morphology assessment.