Garment representation, animation and editing is a challenging topic in the area of computer vision and graphics. Existing methods cannot perform smooth and reasonable garment transition under different shape styles and topologies. In this work, we introduce a novel method, termed as DeepCloth, to establish a unified garment representation framework enabling free and smooth garment style transition. Our key idea is to represent garment geometry by a UV-position map with mask, which potentially allows the description of various garments with different shapes and topologies. Furthermore, we learn a continuous feature space mapped from the above UV space, enabling garment shape editing and transition by controlling the garment features. Finally, we demonstrate applications of garment animation, reconstruction and editing based on our neural garment representation and encoding method. To conclude, with the proposed DeepCloth, we move a step forward on establishing a more flexible and general 3D garment digitization framework. Experiments demonstrate that our method can achieve the state-of-the-art garment modeling results compared with the previous methods.