The perturbative evaluation of the time-dependent quantum transport is investigated by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation in this paper.We obtain the complete set of solutions of the time-dependent Schrdinger equation governing the behaviour of electrons in a double-well structure. Based on these exact solutions,we obtain the first-order quantum rate equation by regarding the interaction Hamiltonian between the double-well structures and the heat reservoirs as the perturbative Hamiltonian.An approach to the geometric phase factor (Berry's phase factor) in the adiabatic quantum transport process is briefly discussed in this paper.We hold that the formulation presented here has advantages in dealing with transport problem over the method proposed by Gurvitz et al.