Electronic quantum entanglement between the central chain and the two electrodes in an infinite one-dimensional two-probe device system is studied. The entanglement entropy is calculated employing the nonequilibrium Green's function method in the tight-binding model based on the relation between the correlation matrix and the von Neumann entropy. By extending the entropy to nonequilibrium cases, we have studied the scaling behavior when a voltage bias is applied between the two electrodes. The entropy usually decreases with the bias and may jump up when a quasi-state in the chain aligns in energy with the band edges in the electrodes. Odd-even effect is observed due to the symmetry of the chain.