The performance of narrowband active noise control (ANC) systems degenerates significantly under the frequency mismatch between the synthesized reference signal and the primary noise. This paper proposes a new narrowband ANC system that incorporates a frequency corrector for the internal reference signal generator to mitigate the ill-effects caused by the frequency mismatch. The proposed frequency estimator uses the iterative frequency estimation algorithm based on the minimum variance distortionless response spectrum that has advantages of accuracy and fast convergence. The performance of the new narrowband ANC system is analyzed under the conditions of frequency mismatch and the secondary-path phase estimation error. The frequency and amplitude of the primary noise are modeled as time-varying variables in the theoretical analysis. Computer simulations are conducted to demonstrate the performance of the new ANC system and to verify the analysis results.