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We make an attempt to address topology-awareness for 3D shape reconstruction. Two types of high-level shape typologies are being studied here, namely genus (number of cuttings/holes) and connectivity (number of connected components), which are of great importance in 3D object reconstruction/understanding but have been thus far disjoint from the existing dense voxel-wise prediction literature. We propose a topology-aware shape autoencoder component (TPWCoder) by approximating topology property functions such as genus and connectivity with neural networks from the latent variables. TPWCoder can be directly combined with the existing 3D shape reconstruction pipelines for end-to-end training and prediction. On the challenging A Big CAD Model Dataset (ABC), TPWCoder demonstrates a noticeable quantitative and qualitative improvement over the competing methods, and it also shows improved quantitative result on the ShapeNet dataset.