Electrospun polyacrylonitrile (PAN) nanofibers were carbonized with or without iron (III) acetylacetonate to induce catalytic graphitization within the range of 900-1,500$^{circ}C$, resulting in ultrafine carbon fibers with a diameter of about 90-300 nm. Their structural properties and morphologies were investigated. The carbon nanofibers (CNF) prepared without a catalyst showed amorphous structures and very low surface areas of 22-31 $m^{2}$/g. The carbonization in the presence of the catalyst produced graphite nanofibers (GNF). The hydrogen storage capacities of these CNF and GNF materials were evaluated through the gravimetric method using magnetic suspension balance (MSB) at room temperature and 100 bar. The CNFs showed hydrogen storage capacities which increased in the range of 0.16-0.50 wt$\%$ with increasing carbonization temperature. The hydrogen storage capacities of the GNFs with low surface areas of 60-253 $m^{2}$/g were 0.14-1.01 wt$\%$. Micropore and mesopore, as calculated using the nitrogen gas adsorption-desorption isotherms, were not the effective pore for hydrogen storage.