This paper proposes a robust adaptive finite-time controller for stabilization of a non-autonomous electromechanical gyrostat system in the presence of model uncertainties and external disturbances. The effect of the dead-zone nonlinearity in the control input is also taken into account. Moreover, all parameters of the system are assumed to be fully unknown in advance. To deal with the system's unknown parameters, some adaptation laws are introduced. Subsequently, based on the finite-time control theory, an adaptive robust controller is proposed to stabilize the non-autonomous gyrostat system in a given finite time. Then, Lyapunov's stability theory is applied to prove the finite-time stability of the designed control scheme. Finally, a numerical simulation is given to demonstrate the efficacy and robustness of the proposed finite-time control approach.