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Given the enormous capital value of power transformers and their integral role in the electricity network, increasing attention has been given to diagnostic and monitoring tools as a safety precaution measure to evaluate the internal condition of transformers. This study overcomes the fault diagnosis problem of power transformers using an ultra high frequency drain valve sensor. A convolutional neural network (CNN) is proposed to classify six types of discharge defects in power transformers. The proposed model utilizes the phase-amplitude response from a phase-resolved partial discharge (PRPD) signal to reduce the input size. The performance of the proposed method is verified through PRPD experiments using artificial cells. The experimental results indicate that the classification performance of the proposed method is significantly better than those of conventional algorithms, such as linear and nonlinear support vector machines and feedforward neural networks, at 18.78%, 10.95%, and 8.76%, respectively. In addition, a comparison with the different representations of the data leads to the observation that the proposed CNN using a PA response provides a higher accuracy than that using sequence data at 1.46%.