The two-dimensional boron monolayers were reported to be metallic both in previous theoretical predictions and experimental observations. Unexpectedly, we have first found a family of boron monolayers with the novel semiconducting property as confirmed by the first-principles calculations with the quasi-particle G(0)W(0) approach. We demonstrate that the connected network of hexagonal vacancies dominates the gap opening for both the in-plane s+p(x,y), and p(z) orbitals, with which various semiconducting boron monolayers are designed to realize the band gap engineering for the potential applications in electronic devices. The semiconducting boron monolayers in our predictions are expected to be synthesized on the proper substrates, due to the similar stabilities to the ones observed experimentally.