Current artificial intelligence faces challenges in improving computational efficiency due to increasing scale and complexity. Superconducting circuit, as one of the most promising technologies in the post-Moore era, offers ultrahigh-speed computation and ultralow power consumption. Superconducting circuits are driven by pulses, which enables direct execution of pulse-based neuromorphic computing. Consequently, superconducting circuits hold the potential to facilitate higher efficiency and larger scale neuromorphic chips. However, existing efforts neglect the limitations and constraints of superconducting circuits, such as the extra overhead of pulse-based logic, the lack of superconducting memory, and low integration. Hence, their work cannot be utilized in fabricating real superconducting neuromorphic chips. This article introduces superconducting spiking neural network (SSNN), which aims to enable full neuromorphic computing on superconducting circuits. The design of SSNN addresses key issues including a superconducting circuit-based neuron model, weight processing methods suitable for superconducting pulses, and superconducting neuromorphic on-chip networks. SSNN enables complete neuromorphic computing on superconducting circuits. We validate the feasibility and accuracy of SSNN using a standard cell library of superconducting circuits and successfully fabricate the world's first superconducting neuromorphic chip. Our evaluation demonstrates a remarkable 50 x increase in power efficiency compared to state-of-the-art semiconductor designs.