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Current-induced heating of short double-stranded DNA chains is studied within a two-probe transport setup by using the Langevin approach. The electrons are modeled by a tight-binding Hamiltonian. The DNA atomic motion is described by the Peyrard–Bishop–Dauxois atomic potential, coupled with electrons through the Holstein interaction. The solvent environment is accounted for as a classical heat bath. Voltage biases of $0.1\sim 0.5\;{\rm{V}}$ can effectively break the base pairs and lead to the melting transition, which can be detected from the resulting significant reduction of the conductance. When the bias increases, the opening of base pairs near the leads with higher chemical potential is suppressed and bubble (localized separation of the double strand) formation becomes asymmetric. Our results suggest that the voltage bias can excite the base pairs, hence increases the chemical activity of DNA.