For the disposal of the high efficiency particulate air (HEPA) glass filter to environment, the glass fiber should be leached to lower its radioactive concentration. To derive the optimum method for removal of Co and Cs from HEPA glass fiber, four methods were applied in this study. Results of electrochemical leaching of glass fiber by 4.0 M HNO3–0.1 M Ce(IV) solution showed that the removal efficiency of 134Cs, 137Cs, and 60Cs from glass fiber after 5 h was 96.4, 93.6, and 93.8%, respectively. Results by 5 wt% NaOH solution showed that the removal efficiency of 134Cs, 137Cs, and 60Cs after 30 h was 81.7, 82.1, and 10.0%, respectively. Results by repeat 2.0 M HNO3 solution showed that the removal efficiencies of 134Cs, 137Cs, and 60Cs after 2 h of three repetitions were 96.2, 99.4, and 99.1%, respectively. Finally, results by repeat 4.0 M HNO3 solution showed that the removal efficiencies of 134Cs, 137Cs, and 60Cs after 4 h of three repetitions were 100, 99.9, and 99.9%, respectively, and their radioactivities were below 0.1 Bq/g. Therefore, the chemical leaching method by 4.0 M HNO3 solution was considered as an optimum one for removal of cesium and cobalt from HEPA glass fiber for self disposal. Also the removal efficiencies of 60Co, 134Cs, and 137Cs from the waste-solution after its precipitation-filtration treatment for reuse of 4.0 M HNO3 waste-solution were 88.0, 95.0, and 99.8%.