The aim of the present work is to develop a numerical model to understand and optimize the process parameters for the growth of carbon nanofibers (CNFs) inside the plasma enhanced chemical vapor deposition system containing acetylene, hydrogen, and argon gases. Two-dimensional axis-symmetrical inductive couple plasma module is implemented using COMSOL Multiphysics 5.2 simulation software to analyze the density profiles and temperatures of electrons, ions, and neutral species in the plasma at different gas pressures and input plasma powers. The outcomes of the COMSOL computational model show that the electron density in the plasma decreases with increase in gas pressure and increases with increase in plasma power. Other than the computational model, an analytical model is developed in the present paper that accounts the plasma sheath equations to study the fluxes and energies of the plasma species. The results obtained from the plasma sheath model at the catalyst-substrate surface boundary are fed as the input parameters to surface deposition model to investigate the growth characteristics of carbon nanofibers, i.e., poisoning of the catalyst nanoparticle, height, and diameter of carbon nanofiber at different gas pressures and input plasma powers. It is found that electron density decays at the faster rate when gas pressure is increased and decays at slower rate when input plasma power is raised. Moreover, it is also found that growth rate of CNFs increases with increase in gas pressure and plasma power. However, the significant drop in CNF growth rate is observed when the gas pressure is high enough (above and around 50 Torr). From the results obtained, it can be concluded that the CNFs having good growth characteristics can be obtained at some optimum pressure range, i.e., one order of the magnitude in the units of Torr. A good comparison between numerical simulation results and analytical results with each other and with existing experimental results confirms the adequacy of the computational and analytical approach.