We report on the magnetic tunneling properties of weakly coupled GaAs/AlGaAs/InGaAs double quantum well tunneling structure at low temperature (15 K) in a magnetic field applied parallel to the tunneling current. The device is in resonance at zero bias voltage. From an analysis of the oscillations in magneto-conductivity for different bias voltages, the change in ground-state energy levels in two quantum wells with the bias can be confirmed and thus the tunneling mechanism was studied. The results reported in this paper provide the basis for the successful fabrication of weakly coupled double quantum dot system.