The conventional narrowband active noise control (ANC) is a popular method for reducing narrowband noise generated from rotating machines like engines, fans, blowers, and power transformers. The narrowband active noise control works efficiently only when the internal reference frequency of the controller and the frequency of the primary noise remains the same. Any change in the frequency of the primary noise from that of the reference is termed as frequency mismatch (FM), which degrades the narrowband ANC performance. In this paper, a filtered-x weighted-frequency Fourier linear combiner least mean square (FX-WFLC-LMS) algorithm is developed for narrowband ANC system. This algorithm is capable of adapting to both frequency and amplitude variations in the primary noise. To reduce the computational burden of the proposed FX-WFLC-LMS algorithm, a computationally efficient filtered-error weighted-frequency Fourier linear combiner least mean square (FE-WFLC-LMS) algorithm is also proposed. The comparative performance of these proposed algorithms is evaluated through extensive simulation and real-time experiments. It was found that both these proposed algorithms are capable of correcting any amount of frequency mismatch and are suitable for narrowband ANC systems.