A family of semiconducting multiporous hexagonal boron nitride foams (HBNFs) with both sp(2) and sp(3) hybridized bonds is presented, which can be achieved by linking armchair BN nanoribbons (A-BNNRs). Based on density functional theory (DFT) calculations, we find that most of these HBNFs are dynamically, thermally and mechanically stable. Their electronic bandgaps vary in a wide range and exponentially change with the ribbon width. Interestingly, the electronic bandgaps of HBNFs can be classified into three groups. We also find that the edge effects affect not only the electronic band structure but also the length of B-N chemical bonds. In addition, the electron localization function of HBNFs are also been evaluated.