The entropy production in a non-equilibrium state based on the reversible Oregonator model of the Belousov-Zhabotinskii (BZ) reaction system has been studied. The reaction affinity and the reaction rate for the individual steps have been calculated by varying the concentrations of key variables in the system. The result shows a linear relationship between the reaction affinity and the reaction rate in the given concentration range. However, the overall entropy calculated on the basic assumption that the entropy in a reaction system corresponds to the summation of a product of reaction affinity and reaction rate of individual steps shows a nonlinearity of the reaction system. The results well agrees with the fact that the entropy production is not linear or complicated function in a non-linear reaction system.