Mono- and few-layer graphenes were grown on Ni thin films by rapid-thermal pulse chemical vapor deposition technique. In the growth steps, the exposure step for 60 s in $H_2$ (a flow rate of 10 sccm (standard cubic centimeters per minute)) atmosphere after graphene growth was specially established to improve the quality of the graphenes. The graphene films grown by exposure alone without $H_2$ showed an intensity ratio of $I_G/I_{2D}$ = 0.47, compared with a value of 0.38 in the films grown by exposure in H2 ambient. The quality of the graphenes can be improved by exposure for 60 s in $H_2$ ambient after the growth of the graphene films. The physical properties of the graphene films were investigated for the graphene films grown on various Ni film thicknesses and on 260-nm thick Ni films annealed at 500 and $700^{circ}C$. The graphene films grown on 260-nm thick Ni films at $900^{circ}C$ showed the lowest $I_G/I_{2D}$ ratio, resulting in the fewest layers. The graphene films grown on Ni films annealed at $700^{circ}C$ for 2 h showed a decrease of the number of layers. The graphene films were dependent on the thickness and the grain size of the Ni films.