By merging DFTB calculations and model-Hamiltonian approaches, we study the stretching-twisting process of poly(GC) DNA oligomers. A local maximum for the transfer integral t between two nearest- neighbor GC pairs is found in the stretching process, which arises from the competition between stretching and twisting. This results in a local maximum for the current in the case that the electrode-DNA coupling is greater than t. Reducing to the values smaller than t gives rise to plateaus in the current. The heights of such plateaus are almost equal to each other.