As the fifth-generation (5G) mobile communication network may not meet the requirements of emerging technologies and applications, including ubiquitous coverage, industrial internet of things (IIoT), ubiquitous artificial intelligence (AI), digital twins (DT), etc., this paper aims to explore a novel space-air-ground integrated network (SAGIN) architecture to support these new requirements for the sixth-generation (6G) mobile communication network in a flexible, low-latency and efficient manner. Specifically, we first review the evolution of the mobile communication network, followed by the application and technology requirements of 6G. Then the current 5G non-terrestrial network (NTN) architecture in supporting the new requirements is deeply analyzed. After that, we proposes a new flexible, low-latency and flat SAGIN architecture, and presents corresponding use cases. Finally, the future research directions are discussed.