•OMIMBr and AOIMBr are modest cathodic inhibitors for mild steel in 0.5 M H2SO4.•AOIMBr shows better corrosion inhibition due to the allyl electron-donating group.•Inhibitor mainly physically adsorbs on steel surface via positively charged N atom.•The adsorption of inhibitor molecules obeys El-Awady thermodynamic–kinetic model. The inhibition performance and mechanism of 1-octyl-3-methylimidazolium bromide (OMIMBr) and 1-allyl-3-octylimidazolium bromide (AOIMBr) for the corrosion of mild steel in 0.5M H2SO4 were investigated using weight loss method, electrochemical measurements, scanning electron microscope (SEM) and quantum chemical calculation. The results revealed that OMIMBr and AOIMBr acted as modest cathodic inhibitors, and due to the electron-donating effect of allyl group, AOIMBr showed better inhibitive performance. The adsorption of both inhibitors on steel surface obeyed El-Awady thermodynamic–kinetic model, thus the thermodynamic and kinetic parameters were calculated and discussed. Moreover, theoretical calculation was used to investigate inhibition mechanism of studied inhibitors.