The Jiangmen Underground Neutrino Observatory (JUNO) is designed to determine the neutrino mass ordering and measure neutrino oscillation parameters. A precise muon reconstruction is crucial to reduce one of the major backgrounds induced by cosmic muons. This article proposes a novel muon reconstruction method based on convolutional neural network (CNN) models. In this method, the track information reconstructed by the top tracker is used for network training. The training dataset is augmented by applying a rotation to muon tracks to compensate for the limited angular coverage of the top tracker. The muon reconstruction with the CNN model can produce unbiased tracks with performance that spatial resolution is better than 10 cm and angular resolution is better than 0.6 degrees. By using a GPU accelerated implementation a speedup factor of 100 compared to existing CPU techniques has been demonstrated.