The dark current and photocurrent(PC) spectrum of Mg-doped GaN thin film were investigated with various bias voltages and temperatures. At high temperature and small bias, the dark current is dominated by holes thermally activated from an acceptor level Al located at about 0.16 eV above the valence band maximum $(E_v)$, The PC peak originates from the electron transition from deep level A2 located at about 0.34 eV above the $E_v$ to the conduction band minimum $(E_ C)$. However, at a large bias voltage, holes thermally activated from A2 to Al experience the field-in-duces tunneling to form one-dimensional defect band at Al, which determines the dark current. The PC peak associated with the transition from Al to $E_ C$ is also observed at large bias voltages owing to the extended recombination lifetime of holes by the tunneling. In the near infrared region, a strong PC peak at 1.20 eV appears due to the hole transition from deep donor/acceptor level to the valence band.