It is important for life safety and scientific research to design new sensing materials for detecting CO, CH4 and CO2 from environment. We theoretically designed a new Cr-doped graphene-like hexagonal borophene (CrB6) as potential sensor material for these gases. Carrying out firstprinciples density-functional calculations, we calculated the adsorption energy, band structure, adsorption distance, charge transfer, charge density difference, density of states and partial density of states of CO, CH4 and CO2 gas molecules absorbed on CrB6 monolayer. The calculated resultsshow that the adsorption behavior of CO is different from those of CH4 and CO2. CO adsorbed on CrB6 monolayer prefers chemisorption while CH4 and CO2 adsorbed on CrB6 monolayer prefers physisorption. As a result, the different adsorption behaviors have significant influence on the band structures and density of states of CrB6 monolayer. We hope that our results can help experimentalists synthesize better sensor materials based on hexagonal borophene.