A 520-nm InGaN diode laser can emit a milliwatt-level, single-frequency laser beam when the applied current slightly exceeds the lasing threshold. The laser frequency was less sensitive to diode temperature and could be finely tuned by adjusting the applied current. Laser frequency was stabilized onto a hyperfine component in an iodine transition through the saturated absorption spectroscopy. The uncertainty of frequency stabilization was approximately 8×10-9 at a 10-s integration time. This compact laser system can replace the conventional green diode-pumped solid-state laser and applied as a frequency reference. A single longitudinal mode operational region with diode temperature, current, and output power was investigated.