We construct a parametrized model to explore the main properties of the star-formation history of M33. We assume that the disc originates and grows by primordial gas infall and adopt a simple form of gas accretion rate with one free parameter, the infall time-scale. We also include the contribution of the gas outflow process. A major update of the model is that we adopt a molecular-hydrogen-correlated star-formation law and calculate the evolution of the atomic and molecular gas separately. Comparisons between the model predictions and observational data show that the model predictions are very sensitive to the adopted infall time-scale, while the gas-outflow process mainly influences the metallicity profile. A model adopting a moderate outflow rate and an inside-out formation scenario can be in good agreement with most of the observed constraints of the M33 disc. We also compare model predictions based on a molecular-hydrogen-correlated star-formation law and that based on the Kennicutt star-formation law. Our results imply that the molecular-hydrogen-correlated star-formation law should be preferred to describe the evolution of the M33 disc, especially the radial distributions of both the cold gas and the stellar population.