The pursuit of high-performance materials for interconnects and electrodes in various electronic applications has led to the exploration of carbon nanotubes (CNTs)-graphene hybrid materials due to their potential to surpass copper (Cu) in terms of thermal conductivity. This study aimed to grow CNTs on graphene. However, the applied growth parameters led to the formation of carbon nanofibers (CNFs) on graphene. CNFs-graphene hybrids may have lower thermal conductivity compared to CNTs-graphene hybrids. This investigation aims to understand the growth evolution of the CNFs at a varied carrier gas flow rate. This work investigates the CNFs' growth on graphene on a nickel (Ni) thin film substrate under a growth temperature of 860°C in 2 hours. By varying the gas flow rate, this research aims to discern the optimal conditions for achieving controllable CNFs growth on graphene. This work found that the higher carrier gas flow rate led to better formation of CNFs with a more uniform coverage and smaller width. The XRD results confirm the formation of CNFs on graphene.