Abstract: For narrowband active noise control (ANC) systems with high sampling frequencies, a simplified narrowband frequency-domain ANC algorithm is proposed that does not require secondary path information. This algorithm directly calculates the amplitude and phase information of the frequency bins corresponding to the reference signal and error signal in the frequency domain by substituting the reference signal sampling points into the discrete Fourier transform (DFT) definition. These frequency bins are evenly divided into multiple sub-frequency bin groups. For each sub-frequency bin group, the optimal update direction for the adaptive filter coefficients is chosen from the four directions of 0°, 180°, and ±90° to achieve narrowband noise reduction. Compared to the FDFxLMS algorithm, the proposed algorithm avoids the participation of all full-band frequency bins in the calculation, thereby improving computational efficiency. When the number of effective frequency bins meets certain conditions, the computational complexity can be reduced. Simulations using single frequency, multi-frequency, and narrowband noise as primary noise sources demonstrate that the proposed algorithm maintains good noise reduction performance while exhibiting excellent stability and tracking characteristics.