Magnesium alloy is regarded as a lightest engineering structural metal material due to its low density, but its wide application is limited due to poor plastic deformation behavior. Therefore, the comprehensive mechanical properties of enhanced magnesium alloy have become a research focus in the material science. Here, the effect of graphene on the deformation behavior and that on the mechanical properties of magnesium under tensile loading are studied by molecular dynamics simulation. The results show that the introduction of graphene can significantly improve the mechanical properties of pure magnesium. Comparing with pure magnesium, the Young's modulus and the first peak stress of the graphene magnesium matrix (GR/Mg) composites are increased by about 27.5% and 36.5% respectively, which is mainly due to the excellent mechanical properties of graphene. The results also indicate that the embedded position of graphene has little effect on the Young's modulus or peak stress of the GR/Mg composites, but it will significantly affect the plastic deformation behavior of the GR/Mg composites after the second peak stress. With the increase of the embedded height of graphene, the average flow stress of the GR/Mg composites first increases in the later stage of plastic deformation. When the embedded height reaches 0.4L, the average flow stress of the GR/Mg composites reaches a maximum value, and then decreases. This phenomenon of the Gr/Mg composites can be explained by the plastic deformation behavior of the magnesium matrix above and below graphene. The embedded position of graphene has a great influence on the plastic deformation behavior of the upper and lower magnesium matrix of the GR/Mg composites. When the embedded height of graphene is small, the plastic deformation capability of magnesium matrix under graphene is strong and dislocation slip is easy to occur. And when the embedded height of graphene is large, the plastic deformation capabilities of the two parts of magnesium matrix above and below graphene are equal, and their plastic deformation behavior tends to be synchronous. The results show that the plastic deformation behavior of the GR/Mg composite is the same as that of pure magnesium, and the phase transition from HCP to BCC and then to HCP occurs in the process of the plastic deformation. The phase transition mechanism of magnesium matrix is also analyzed in detail. The results of this study have certain theoretical guiding significance in designing the high performance graphene metal matrix composites.