Detecting candidates of supernova remnants (SNRs) in the interstellar medium (ISM) is a challenging task because of their weak radio signals and irregular shapes. A convolutional neural network (CNN) is a deep learning method that can extract image features from the SNRs regions. In this study, we design the SNR-Net model, which comprises a training component and a detection component, to extract characteristic features from observations and calculate the position of candidate SNRs. In addition, migration learning is used to initialize the network parameters, which improves the speed and accuracy of network training. We apply the T-T plot method (the different brightness temperatures of map pixels at two different frequencies) to compute the spectral index of candidate SNRs areas. To accelerate the scientific computing process, we also take advantage of innovative hardware architecture, such as deep learning optimized GPUs, which increase the speed of computation by a factor of five. This case study suggests that SNR-Net may be applicable to detecting extended sources in the ISM a task that has so far proven difficult to automate.