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The electronic structures of hexagonal boron nitride (BN) bilayers are studied by first principles calculations. The stabilities of BN bilayers with various stackings are determined. We find that an external electric field could significantly modulate the energy gaps of BN bilayers. By a relatively small adjustment of interlayer distance near the equilibrium position, we show that the direct band gaps can be obtained in a wide energy range when an external electric field is applied. These results suggest potential applications of BN bilayers in light emitting devices.