Due to the high noise of Positron Emission Tomography (PET), the existing image denoising effect is not ideal. Therefore, a new method combining residual U-Net neural network and Deep Image Prior (DIP) is proposed. Firstly, residual learning is introduced into the U-Net network to improve the network expression ability and convergence speed. Then, a DIP algorithm without training data is proposed. The neural network is interpreted as the parameterization of the image, and the noise is removed by using the high impedance characteristics of the parameterized noise to achieve the purpose of noise reduction. Finally, the real data obtained from the brains of living monkeys injected with 18f-2-fluorodeoxyglucose (18F-FDG) were used for simulation analysis. The results show that the proposed method can get a clear and smooth image. In different noise levels and time frames, the denoising effect of the proposed method is better than other contrast methods, and can obtain high-quality images.