Abstract: One of the biggest challenges to the reliability of quantum computers is decoherence caused by the interaction between local environment and quantum bits. Among the major approaches being pursued for realizing quantum bits, the Majorana-based platform has attracted increasing interest in recent years since it stores quantum information in a topologically-protected manner. The quantum information is protected by its nonlocal storage in localized and well-separated Majorana zero modes, which is expected to solve the problem of quantum decoherence. Semiconductor-superconductor hybrid nanowires are promising platforms for studying Majorana zero modes and topological quantum computation. This article reviews the recent progress of the in-situ molecular-beam epitaxial growth and low-temperature quantum transport properties of the high-quality semiconductor-superconductor nanowires. The prospects of the topological quantum computing based on semiconductor-superconductor nanowires are also prospected finally.