An amount of reducing agent adsorbed on a NOx catalyst when a reducing agent supply device is normal and a corresponding detected value may be estimated. The corresponding detected value may be detected by a NOx sensor, and the detected value may correspond to an amount of reducing agent adsorbed on the NOx catalyst. When the estimated amount of adsorption is larger than or equal to a first amount and is smaller than or equal to a second amount, a diagnosis of the NOx catalyst based on the detected value of the NOx sensor may be prevented. The first amount may be an amount of adsorbed reducing agent corresponding to a minimum value of the corresponding detected value. The second amount may be an amount of adsorbed reducing agent corresponding to the corresponding detected value when the amount of adsorbed reducing agent is zero and larger than the first amount.