A method to manufacture a carbon fiber electrode comprises synthesizing polyamic acid (PAA) as a polyimide (PI) precursor from pryomellitic dian hydride (PMDA) and oxydianiline (ODA) as monomers and triethylamine (TEA) as a catalyst, adding dimethylformamide (DMF) to the polyamic acid (PAA) solution to prepare a spinning solution and subjecting the spinning solution to electrostatic spinning at a high voltage to obtain a PAA nanofiber paper, converting the PAA nanofiber paper into a polyimide (PI) nanofiber paper by heating, and converting the polyimide (PI) nanofiber paper into a carbon nanofiber (CNF) paper by heating under an Ar atmosphere. Also, the method to manufacture a polyimide carbon nanofiber electrode and/or a carbon nanotube composite electrode may utilize carbon nanofibers having diameters that are lessened by optimizing electrostatic spinning in order to improve spinnability.