In this working, we introduce a Q-DD composed of two QDs. We find that the absorption and dispersion spectra of the light pulse can be changed via the effect of and inter-dot tunnel couplings and probe pumping field of QDs. Then, we employ the steady state and dynamical state in the four-level double QDs system. The slope of dispersion switches from positive to negative. Therefore, both superluminal and Subluminal light propagations can be achieved by simply applying a gate voltage to the double inter dot tunnel coupling. It is also demonstrated that by applying the indirect pump probe field to the probe transition the absorption-free superluminal light propagation is obtained. The results show that by proper tuning of the bias voltage. This structure also indicates that a wide range of linearity from negative to positive can be simply adjusted via a bias voltage, which would result in wide control of signal beam.