This paper presents a novel parameter calibration approach for power system stability models using automatic data generation and advanced deep learning technology. A PMU-measurement-based event playback approach is used to identify potential inaccurate parameters and automatically generate extensive simulation data, which are used for training a convolutional neural network (CNN). The accurate parameters will be predicted by the well-trained CNN model and validated by original PMU measurements. The accuracy and effectiveness of the proposed deep learning approach have been validated through extensive simulation and field data.