Two types of modifications were performed on a commercial polyimide (PI) hollow fiber membrane for carbon dioxide ($CO_2$) and methane ($CH_4$) gas permeations. Thermal annealing was conducted between 50- and $200^{circ}C$ while chemical cross-linking was performed using 0.1- to 1.0 wt% of N, (1-Naphthyl) ethylene-diamine dihydrochloride (NED). Membrane characterization revealed densification of the thermally annealed PIs. But formation of macrovoids was observed in PIs annealed near its glass transition temperature ($207^{circ}C$). Fourier transform infrared spectroscopy confirmed the successful cross-linking of NED with PI. Highest $CO_2$ permeance was obtained from pristine PI (P/L=225 GPU) but it also had the lowest selectivity (${alpha}$=72). The performances of thermally annealed (P/L=160-219 GPU, ${alpha}$=76-106), NED crosslinked (P/L=68-139 GPU, ${alpha}$=65-95) and thermally induced NED cross-linked (P/L=51-91 GPU, ${alpha}$=98-138) PIs varied according to modification conditions. Among the modified membranes, highest $CO_2$ permeance was obtained from thermally annealed PI at $100^{circ}C$ (P/L=211GPU, ${alpha}$=106) while thermally induced NED cross-linked PI ($100^{circ}C$, 0.5 wt% NED) exhibited the highest selectivity (P/L=91, ${alpha}$=138). Both modified membranes are the best candidates for $CO_2/CH_4$ separation.