We propose a novel integral probability metric-based generative adversarial network (GAN), called SphereGAN. In the proposed scheme, the distance between two probability distributions (i.e., true and fake distributions) is measured on a hypersphere. Given that its hypersphere-based objective function computes the upper bound of the distance as a half arc, SphereGAN can be stably trained and can achieve a high convergence rate. In sphereGAN, higher-order information of data is processed using multiple geometric moments, thus improving the accuracy of the distance measurement and producing more realistic outcomes. Several properties of the proposed distance metric on the hypersphere are mathematically derived. The effectiveness of the proposed SphereGAN is demonstrated through quantitative and qualitative experiments for unsupervised image generation and 3D point cloud generation, demonstrating its superiority over state-of-the-art GANs with respect to accuracy and convergence on the CIFAR-10, STL-10, LSUN bedroom, and ShapeNet datasets.