Sublimation of SiC substrates is a promising way to prepare high-quality graphene on large scale. Nowadays, growth of high-quality epitaxial graphene is still a crucial issue. In this work, monolayer epitaxial graphene is grown on Si-terminated 4H-SiC (0001) substrate. By introducing argon inert gas and silicon vapor as background atmosphere, the Si evaporation rate and condensation rate on the SiC surface is close to equilibrium and the growth of monolayer epitaxial graphene with very low speed is realized. The growth duration of monolayer epitaxial graphene is prolonged to 75 minutes from 15 minutes. It is found that the disorder-induced Raman D peak shows an obvious decrease as the growth speed decreases, indicating the improvement of crystal quality, which makes the electrical properties of the monolayer epitaxial graphene is improved. The maximum carrier mobility and sheet resistance have reached 1200 cm2/Vs and 604 /, respectively. The above results indicate that slowing down of growth speed by controlling of growth atmosphere is an efficient way to prepare high-quality epitaxial graphene.