A correction method of NOx purifying efficiency of SDPF includes: measuring a temperature change per unit time inside the SDPF, determining whether the temperature change per unit time inside the SDPF is below a first predetermined value, determining whether a difference between a maximum value and a minimum value of temperature of respective parts inside the SDPF is below a second predetermined value if the temperature change per unit time inside the SDPF is below the first predetermined value, determining whether a temperature inside the SDPF is in a low temperature region if the difference between the maximum value and the minimum value of temperature of the respective parts inside the SDPF is below the second predetermined value, and performing a low temperature region correction if the temperature inside the SDPF is in the low temperature region.