Two-dimensional (2D) semiconductors with desirable bandgaps and high carrier mobility have great potential in electronic and optoelectronic applications. In this work, we proposed α-TeB and β-TeB monolayers using density functional theory (DFT) combined with the particle swarm-intelligent global structure search method. The high dynamical and thermal stabilities of two TeB structures indicate high feasibility for experimental synthesis. The electronic structure calculations show that the two structures are indirect bandgap semiconductors with bandgaps of 2.3 and 2.1 eV, respectively. The hole mobility of the β-TeB sheet is up to 6.90 × 102 cm2 V-1 s-1. By reconstructing the two structures, we identified two new horizontal and lateral heterostructures, and the lateral heterostructure presents a direct band gap, indicating more probable applications could be further explored for TeB sheets.