The electrical properties of the GaN-based green light emitting diodes(LEDs) with the Mg-doped p-GaN layer activated in $N_2$ or $O_2$ ambient have been compared. For the $N_2$ -ambient activation the current-voltage behavior of LEDs has been found to be improved when the Mg dopants activation was performed in the higher temperature. However, for the $O_2$-ambient activation the current-voltage characteristic has been observed to be enhanced when the Mg dopants activation was carried out in the lower temperature. The minimum forward voltage at 20mA was obtained to be 4.8 V for LEDs with the p-GaN layer activated at $900^{circ}C$ in the $N_2$ ambient and 4.5V for LEDs with the p-GaN layer treated at $700^{circ}C$ in the $O_2$ambient, repectively. The forward voltage reduction of the LEDs treated in the $O_2$-ambient may be related to the oxygen co-doping of the p-GaN layer during the activation process. The $O_2$ -ambient activation process is useful for the enhancement of the LED performance as well as the fabrication process since this process can activate the Mg dopants in the low temperature.