The fundamental properties of graphene are making it an attractive material for a wide variety of applications. Various techniques have been developed to produce graphene and recently we discovered the synthesis of large area graphene by chemical vapor deposition (CVD) of methane on Cu foils. We also showed that graphene growth on Cu is a surface-mediated process and the films were polycrystalline with domains having an area of tens of square micrometers. In this paper, we report on the effect of growth parameters such as temperature, and methane flow rate and partial pressure on the growth rate, domain size, and surface coverage of graphene as determined by Raman spectroscopy, and transmission and scanning electron microscopy. On the basis of the results, we developed a two-step CVD process to synthesize graphene films with domains having an area of hundreds of square micrometers. Scanning electron microscopy and Raman spectroscopy clearly show an increase in domain size by changing the growth parameters. Transmission electron microscopy further shows that the domains are crystallographically rotated with respect to each other with a range of angles from about 13 to nearly 30°. Electrical transport measurements performed on back-gated FETs show that overall films with larger domains tend to have higher carrier mobility up to about 16000 cm2 V−1 s−1 at room temperature.