3D object reconstruction is important for semantic scene understanding. It is challenging to reconstruct detailed 3D shapes from monocular images directly due to a lack of depth information, occlusion and noise. Most current methods generate deterministic object models without any awareness of the uncertainty of the reconstruction. We tackle this problem by leveraging a neural object representation which learns an object shape distribution from large dataset of 3d object models and maps it into a latent space. We propose a method to model uncertainty as part of the representation and define an uncertainty-aware encoder which generates latent codes with uncertainty directly from individual input images. Further, we propose a method to propagate the uncertainty in the latent code to SDF values and generate a 3d object mesh with local uncertainty for each mesh component. Finally, we propose an incremental fusion method under a Bayesian framework to fuse the latent codes from multi-view observations. We evaluate the system in both synthetic and real datasets to demonstrate the effectiveness of uncertainty-based fusion to improve 3D object reconstruction accuracy.