This paper presents combination of Graph Fourier Trans- form (GFT) and U-net, proposes a deep neural network (DNN) named G-Unet for single channel speech enhancement. GFT is carried out over speech data for creating inputs of U-net. The GFT outputs are combined with the mask estimated by U- net in time-graph (T-G) domain to reconstruct enhanced speech in time domain by Inverse GFT. The G-Unet outperforms the combination of Short time Fourier Transform (STFT) and mag- nitude estimation U-net in improving speech quality and de- reverberation, and outperforms the combination of STFT and complex U-net in improving speech quality in some cases, which is validated by testing on LibriSpeech and NOISEX92 dataset.