Existing methods for single-view 3D object reconstruction directly learn to transform image features into 3D representations. However, these methods are vulnerable to images containing noisy backgrounds and heavy occlusions because the extracted image features do not contain enough information to reconstruct high-quality 3D shapes. Humans routinely use incomplete or noisy visual cues from an image to retrieve similar 3D shapes from their memory and reconstruct the 3D shape of an object. Inspired by this, we propose a novel method, named Mem3D, that explicitly constructs shape priors to supplement the missing information in the image. Specifically, the shape priors are in the forms of "image-voxel" pairs in the memory network, which is stored by a well-designed writing strategy during training. We also propose a voxel triplet loss function that helps to retrieve the precise 3D shapes that are highly related to the input image from shape priors. The LSTM-based shape encoder is introduced to extract information from the retrieved 3D shapes, which are useful in recovering the 3D shape of an object that is heavily occluded or in complex environments. Experimental results demonstrate that Mem3D significantly improves reconstruction quality and performs favorably against state-of-the-art methods on the ShapeNet and Pix3D datasets.