The results of a parametric study on the growth of vertically aligned carbon nanofibers (CNFs) by high-density inductively coupled plasma (ICP) chemical-vapor deposition are reported. We investigated the mechanisms that cause the detachment of CNFs during the growth process by high-density plasma-enhanced chemical-vapor deposition with high substrate bias voltage and atomic hydrogen concentration. A simplified model, combining the Child law for sheath field, floating sphere model for field enhancement at the fiber tip and electric-field screening effect, was employed to estimate the detachment electrostatic force on individual CNFs induced by plasma sheath electric field. The force was found to increase with substrate bias voltage, bias current, and lengths of CNFs, consistent with the experimental observations that CNFs density decreases with ICP power, bias power, and growth time. However, the magnitude of the electrostatic force per se cannot explain the detachment phenomena. The other factor is believed to be the ion-assisted etch of CNFs by atomic hydrogen during the growth process since it was observed that the lower end of CNFs formed earlier in the synthesis process became thinner than the tip end.