Numerical simulations have been conducted for the cylindrical steam reformer having various boundary temperature distributions. $CH_4$, $H_2O$, CO, $H_2$ and $CO_2$ are often generated or destroyed by the reactions, namely the Steam Reofrming(SR) reaction, the Water-Gas Shift (WGS) reaction and the Direct Steam Reforming(DSR) reaction. The SR and the DSR reactions are endothermic reactions, and the WGS reaction is an exothermic reaction. The rate of reactions can be slightly controlled by artificially given boundary temperature distributions. Therefore, the component ratio of the gases at the outlet are different for various boundary temperature distributions, namely the constant, cubic and linear distributions. Among these distributions, the linear temperature distribution is outstanding for efficient hydrogen production of the steam reformer.