Sensitive materials for formaldehyde (HCHO) sensor need high sensitivity and selectivity. The research on two dimensional (2D) sensitive material is growing, and most studies focus on the pristine or modified graphene. So it is essential to introduce other 2D materials into HCHO gas sensor. In this report, the adsorption behaviors of organic gas molecules including C2H6, C2H4, C2H2, C6H6, C2H5OH and HCHO over indium triphosphide (InP3) monolayer were studied by using first-principle atomistic simulations. The calculation results demonstrate that InP3 monolayer has a high sensitivity and selectivity to HCHO than others. By comparing the structures and adsorption results of InP3 monolayer, graphene and single-layered MoS2, it was found that the polarity bonds and steric effect of the site on monolayer play an important role in the detection of HCHO. The effect of strain on the gas/substrate adsorption systems was also studied, implying that the stained InP3 monolayer could enhance the sensitivity and selectivity to HCHO. This study provides useful insights into the gas-surface interaction that may assist future experimental development of 2D material for HCHO sensing and performance optimization based on strain.