A one-dimensional heterogeneous fixed-bed methanol synthesis reactor model was developed for the optimization of carbon conversion and rate of methanol production. The developed model was validated both at pellet and reactor scales. The reactor inlet syngas composition and cooling water temperature, i.e., the design variables, providing the highest carbon conversion and rate of methanol production were determined by a constrained derivative-free optimization algorithm. The results revealed that after optimization the carbon conversion was increased by 12 % and the rate of methanol production by 48 %. Under the optimized conditions, the stoichiometric number was in the range of industrial values.