The electronic properties of hexagonal boron nitride (h-BN) are controllable by applying normal pressure. In this work, we perform first -principles density functional calculation to investigate electronic structure of several h-BN bilayers with different stacking patterns under normal pressure. The results suggest that the band gap of h-BN bilayer, surprisingly, undergoes both decreasing and increasing trend with increasing of normal pressure, which is considerably different from monotonously decreasing by applying electric field. Furthermore, it is found that the transformation from a direct-to an indirect-gap can be achieved in the case of stacking pattern II as the pressure above 34.3%. However, the insulator-semiconductor transition can be induced for stacking pattern I and III under similar normal pressure. The studies indicate a unique yet easy pathway to tune the electronic properties of h-BN by normal pressure, which may pave the way for their potential applications as optoelectronic device materials.