DNA is a promising molecule for applications in molecular electronics because of its unique electronic and self-assembly properties. Here we report that the conductance of DNA duplexes increases by approximately one order of magnitude when its conformation is changed from the B-form to the A-form. This large conductance increase is fully reversible, and by controlling the chemical environment, the conductance can be repeatedly switched between the two values. The conductance of the two conformations displays weak length dependencies, as is expected for guanine-rich sequences, and can be fit with a coherence-corrected hopping model. These results are supported by ab initio electronic structure calculations that indicate that the highest occupied molecular orbital is more disperse in the A-form DNA case. These results demonstrate that DNA can behave as a promising molecular switch for molecular electronics applications and also provide additional insights into the huge dispersion of DNA conductance values found in the literature.