A method of calculating a nitrogen oxide (NOx) mass reduced from a lean NOx trap (LNT) during regeneration includes calculating a C3H6 mass flow used to reduce the NOx among a C3H6 mass flow flowing into the LNT of an exhaust purification device, calculating a NH3 mass flow used to reduce the NOx among a NH3 mass flow generated in the LNT, calculating a reduced NOx mass flow based on the C3H6 mass flow used to reduce the NOx and the NH3 mass flow used to reduce the NOx, and calculating the reduced NOx mass by integrating the reduced NOx mass flow over a regeneration period.