Single-layered III-VI compounds have potential applications in many fields, such as highly sensitive photodetectors, field effect transistors, and electrochemical sensors, due to their wide range photosensitivities and excellent electronic properties. This paper presents a new two-dimensional tetragonal allotrope (called haeckelites structure) of single layered group III monochalcogenides MX( M= Al, Ga, In; X= S, Se, Te), which are constructed from the square and octagon rings. The first-principles calculations are performed using the Vienna abinitio simulation package (VASP) based on density functional theory (DFT). The cohesive energy of the haeckelite structure MXis positive and a little smaller than that (0.07—0.10 eV) of the hexagonal MX. The phonon spectra for the haeckelites structure MXhave basically no imaginary frequencies in the whole Brillouin zone. The calculated binding energy and phonon spectrum show that these structures are energetically and dynamically stable. For all the compounds, the charge density isosurfaces show that most electrons are localized at the positions of Xand Matoms, indicating that the M—Xbond is ionic and M—Mbond is covalent. All of haeckelite structure MXare indirect bandgap semiconductors, and their band gap sizes decrease with the Xatom changing from S to Se to Te. For example, the band gaps of InS, InSe, and InTe are 2.42, 2.07, and 1.88 eV, respectively. The calculation results show that these materials have a wide band gap range from 1.88 to 3.24 eV. We find that the band gaps of AlS, AlSe, and GaS are relatively large with the values of 3.08, 3.03, and 3.24 eV, respectively. This may make them suitable for optically transparent devices. The band structures of GaSe, InS, InSe, and InTe can be further modulated by the biaxial strains. Their band gaps decrease linearly with the strain increasing. The band gap of AlS and AlSe both first increase and then decrease with the strain increasing.