Due to the need to interact with virtual objects, the hand-object interaction has become an important element in mixed reality (MR) applications. In this paper, we propose a novel approach to handle the occlusion of augmented 3D object manipulation with hands by exploiting the nature of hand poses combined with tracking-based and model-based methods, to achieve a complete mixed reality experience without necessities of heavy computations, complex manual segmentation processes or wearing special gloves. The experimental results show a frame rate faster than real-time and a great accuracy of rendered virtual appearances, and a user study verifies a more immersive experience compared to past approaches. We believe that the proposed method can improve a wide range of mixed reality applications that involve hand-object interactions.