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Recent artificial intelligence-based methods have shown great promise in the use of neural networks for real-time sensing and detection of transmission line faults and estimation of their locations. The expansion of power systems including transmission lines with various lengths have made a fault detection, classification, and location estimation process more challenging. Transmission line datasets are stream data which are continuously collected by various sensors and hence, require generalized and fast fault diagnosis approaches. Newly collected datasets including voltages and currents might not have enough and accurate labels (fault and no fault) that are useful to train neural networks. In this paper, a novel transfer learning framework based on a pre-trained LeNet-5 convolutional neural network is proposed. This method is able to diagnose faults for different transmission line lengths and impedances by transferring the knowledge from a source convolutional neural network to predict a dissimilar target dataset. By transferring this knowledge, faults from various transmission lines, without having enough labels, can be diagnosed faster and more efficiently compared to the existing methods. To prove the feasibility and effectiveness of this methodology, seven different datasets that include various lengths of transmission lines are used. The robustness of the proposed methodology against generator voltage fluctuation, variation in fault distance, fault inception angle, fault resistance, and phase difference between the two generators are well shown, thus proving its practical values in the fault diagnosis of transmission lines.