When mobile phones and digital cameras are used to capture information on a screen or store scenes with rich textures, an unpleasant moiré phenomenon occurs, which seriously degrades the quality of the image and affects subsequent image processing tasks. Therefore, to remove the moiré patterns, we propose a multilevel wavelet nested UNet++ demoiréing residual network called MUNet++. Unlike these methods based on the RGB domain, our method is performed in the frequency domain. The multilevel discrete wavelet transform (DWT) and the inverse discrete wavelet transform (IDWT) are elegantly embedded into the UNet++ encoder-decoder structure and transformed to the multilevel frequency domain, which captures more moiré features and preserves details of the image. In addition, we design a dual branch efficient pixel fusion attention module (DBEPFAM) that combines multiscale information, channel attention and the proposed pixel attention fusion module (PAFM) to improve the representation of features. In the network layer, a simple nonlinear unit (NU) is designed and embedded in the middle of the network layer to improve the representation capability of the network. Experimental results on two public datasets show that MUNet++ can effectively remove the moiré patterns and outperform existing state-of-the-art techniques.