Monolayer transition metal dichalcogenide (TMD) alloys with tunable direct band gaps have promising applications in nanoelectronics and optoelectronics. The composition-dependent band gaps of ternary, quaternary and quinary monolayer TMD alloys have been systematically studied combining density functional theory and machine learning models in the present study. The excellent agreement between the DFT-calculated band gaps and the ML-predicted values for the training, validation and test datasets demonstrates the accuracy of our machine learning based on a neural network model. It is found that the band gap bowing parameter is closely related to the difference between the band gaps of the endpoint material compositions of the monolayer TMD alloy and increases with increasing band gap difference. The band gap bowing effects of monolayer TMD alloys obtained by mixing different transition metals are attributed to the conduction band minimum positions, while those of monolayer TMD alloys obtained by mixing different chalcogen atoms are dominated by the valence band maximum positions. This study shows that monolayer TMD alloys with tunable direct band gaps can provide new opportunities for band gap engineering, as well as electronic and optoelectronic applications.