In recent years, another two-dimensional (2D) family, monolayer metal monochalcogenides (group IIIA-VIA), has attracted extensive attention. In this work, we adopt density functional theory (DFT) and the non-equilibrium Green's function (NEGF) method to systematically investigate the ballistic thermoelectric properties of the IIIA-VIA family, including GaS, GaSe, GaTe, InS, InSe, and InTe. Among others, the InTe monolayer possesses the highest figure of merit, ZT = 2.03 at 300 K, due to its ultra-low thermal conductance. Biaxial strain in the range of -10% (compressive) to 10% (tensile) is applied to the InTe monolayer and the strain-induced electronic and thermal transport properties are discussed. The maximum ZT (up to 2.7) for the InTe monolayer at 300 K is achieved under an 8% tensile strain.