A selective catalytic reduction (SCR) catalyst control system and method for an engine is disclosed. Urea injection to an SCR catalyst is determined based on an SCR catalyst model, which determines a value of stored NH3 in the SCR catalyst based on the NOx engine emission value, the SCR catalyst temperature, the quantity of urea supplied to the SCR catalyst and a pre-determined efficiency of conversion of NOx gases. A target value of stored NH3 and the value of stored NH3 in the SCR catalyst is then used to determine a stored NH3 differential, which is then used to calculate urea injection.