Disclosed are a method of correcting a control logic of a selective catalytic reduction (SCR) catalyst and an exhaust system. The control logic may be adapted to calculate an injection amount of a reducing agent for the SCR catalyst at the least. The method may include detecting input variables including temperature of the SCR catalyst and exhaust flow rate, discretizing the input variables, standardizing the discretized input variables, determining whether the discretized input variables are within a correction range, and correcting the control logic of the SCR catalyst if the discretized input variables are within the correction range.