Boron atoms possess a short covalent radius and the flexibility to adopt sp2 hybridization, which favour the formation of diverse two-dimensional allotropes of boron. Several examples of such boron sheets with metallic nature have been reported recently. However, a semiconducting boron crystal with a direct bandgap is rarely reported either in bulk boron crystals or in two-dimensional boron sheets. Here, the boron sheets with a direct bandgap are synthesized on a Ni foil substrate by chemical vapor deposition. The boron sheets with 48 boron atoms per unit cell have a quasicubic structure, and they are semiconducting and have a direct bandgap of around 2.4 eV, which are verified by combining theoretical and experimental investigations. The result greatly expands the known allotropy of the fifth element and opens vast opportunities to design 2D boron sheets with tunable optical, electronic, magnetic and chemical properties.