Point clouds are often sparse and incomplete, which imposes difficulties for real-world applications, such as 3D object classification, detection and segmentation. Existing shape completion methods tend to generate coarse shapes of objects without fine-grained details. Moreover, current approaches require fully-complete ground truth, which are difficult to obtain in real-world applications. In view of these, we propose a self-supervised object completion method, which optimizes the training procedure solely on the partial input without utilizing the fully-complete ground truth. In order to generate high-quality objects with detailed geometric structures, we propose a cascaded refinement network (CRN) with a coarse-to-fine strategy to synthesize the complete objects. Considering the local details of partial input together with the adversarial training, we are able to learn the complicated distributions of point clouds and generate the object details as realistic as possible. We verify our self-supervised method on both unsupervised and supervised experimental settings and show superior performances. Quantitative and qualitative experiments on different datasets demonstrate that our method achieves more realistic outputs compared to existing state-of-the-art approaches on the 3D point cloud completion task.