Low-pressure chemical vapor deposition (LPCVD) is the most efficient method to synthesize large-scale, high-quality graphene for many potential applications such as flexible electronics, solar cells, and separation membranes. The quality of LPCVD is affected by process variables including methane/hydrogen (CH4/H2) ratio, time, pressure, temperature, and cooling rate. The cooling rate has been recognized as one of the most important process variables affecting the amount of carbon source, nucleation, reaction time, and thus the quality of the LPCVD. In this research, we investigate the effect of cooling rate on the quality of graphene synthesize by changing the cooling rate and the gas feeding time. Graphene coverage is measured by Raman mapping. It is found that fast cooling rate leads to decreased carbon source reaction time, which in turn results in higher coverage by monolayer graphene. The temperature-dependent gas feeding time corresponding to different cooling rates can be used to properly supply the carbon source onto the copper surface, also leading to a higher graphene coverage.