Abstract: A solid catalyst containing a potassium component and an iron oxide component, which is such that the ratio of the pore volume of pores therein having a diameter of from 20 to 100 nm to that of pores therein having a diameter of up to 100 nm falls between 0.7/1 and 0.9/1 and which is stable to oxygen-containing vapor, is favorably used as a dehydrogenation catalyst in producing vinyl-aromatic hydrocarbons from alkyl-aromatic hydrocarbons. The catalyst has high initial activity and good initial selectivity and its life is long. In addition, it is easy to handle. The catalyst may be produced by reducing a potassium component-containing iron oxide composition with hydrogen at a temperature falling between 350 and 600° C., and then oxidizing it with an oxygen molecules-containing vapor at a temperature falling between 250 and 500° C.