The wrapped phase is a precondition for obtaining phase information in laser interferometry. In order to reduce the interference of noise in the wrapped phase fringe during measurement and improve the quality of reconstructed image， an asymmetric fusion non-local and verge extraction neural network （AFNVENet） was proposed. The network was designed to add an asymmetric fusion non-local block and a verge extraction module based on FFDNet. By incorporating the noise features with different levels and reverse-guiding the denoising process， it could effectively suppress the noise with different levels while retaining more image details. The wrapped phase dataset with multiplicative speckle and additive random noise was selected to train. The results of ablation and comparative experiments show that AFNVENet algorithm has better noise filtering effect for different level noises. When the noise standard deviation changes in the range of ［0， 2.0］， the means of PSNR， SSIM and SSI are 24.88 dB， 0.97 and 0.95 after noise suppression， respectively. In addition， the unwrapped phase results further show that the RMSE mean of unwrapped phase denoised by AFNVENet is reduced by 87%， 73%， 79% and 36%， respectively， compared to SCAF， NLM， KSVD and DnCNN. The feasibility of method is verified. The AFNVENet method has better robustness in suppressing noises. It is suitable for recovering the wrapped phase information with multilevel noises in different interferometric environments.