Two-dimensional atomic crystal materials have similar lattice structures and physical properties to graphene, providing a broad platform for the scientific research of nanoscaled devices. The emergence of two-dimensional materials presents the new hope of science and industry. As is well known, graphene is the most widely studied two-dimensional (2D) material in recent ten years. Its unique atomic structure and electronic band structure make it have novel physical and chemical properties and broad applications in electronic devices, optical devices, biosensors, solar cell, and lithium ion battery. In recent years, graphene-like single-layered 2D materials have attracted much attention. Researches of these 2D atomic crystal materials and their physical properties, on the one hand, are expected to make up for the lack of band gap in graphene, and on the other hand, continue to explore their unique properties, expand the application of 2D atomic crystal materials. Among all the preparation methods of single-layered 2D atomic crystal materials, the molecular beam epitaxy (MBE) is considered to be the most competitive method. The manufacturing process of MBE is usually carried out under ultra-high vacuum condition, which ensures the cleanness of the 2D material surface. At the same time, the solid growth substrate needed for epitaxial growth can be used as a carrier to support and stabilize the growth of 2D materials. In this review, we summarize many single-layered 2D materials prepared by MBE under ultra-high vacuum conditions in recent years, including monatomic 2D atomic crystal materials (silicene, germanene, stanene, hafnene, borophene, phosphorene, bismuthene, antimonene) and binary atomic crystal materials (hexagonal boron nitride, transition metal dichalcogenides, copper selenide, silver telluride). In addition, by scanning tunneling microscopy (STM), low-energy electron diffraction (LEED) and first-principles calculations, we investigate the atomic structures, energy gap modulations, and electrical properties of 2D materials. These 2D atomic crystal materials exhibit the excellent physical properties, which will make them have broad application prospects in future electronic devices. Finally, we summarize the problems faced by the further development of 2D materials and suggest several potential development directions.