We study the nucleation and growth dynamics of graphene grown on Cu and CuO substrates in a cold wall rapid thermal chemical vapor deposition (RTCVD) system under low pressure. Through image processing and analysis, we quantitatively characterize the RTCVD process. Larger and more compact graphene grains are found on CuO substrate. Furthermore, contrary to the hot wall CVD which exhibit instantaneous nucleation characteristics, our system exhibit substrate dependent non-constant nucleation rates. The coverage evolution can be well described by Johnson-Mehl-Avrami-Kolmogorov (JMAK) model, with the exponent varies from 3.9 to 2.1 for Cu and CuO substrate, respectively. Putting the measured fractal dimensions into the JMAK model, we find exponents related to non-equilibrium nucleation rates that qualitatively agree with observations. Our analysis suggests that new nucleation centers are more efficiently suppressed on CuO substrate during the RTCVD process.