In this advanced world the usage of cutting-edge technologies in daily life increase day by day, whereby, acoustics noise also increases thereby affecting our life. So, an urgent requirement is to reduce this noise and improve the quality of life. Several Active noise control (ANC) systems using Artificial Neural Networks (ANN) are present but in limited performance. This paper is focused to develop an adaptive all-pass filtered x least square algorithm for a single-channel narrowband active noise control system using Nonlinear autoregressive with external (exogenous) input (NARX). The novelty of this research is that the All-pass filtered x LMS (APFxLMS) algorithm is introduced to the system without the need to identify the secondary path. Here the first-order all-pass filters with a single parameter are used to improve the convergence of the LMS algorithm. The results show that the proposed method performance is better in terms of regression and mean square error and on comparison with the recent method through numerical simulation shows that the proposed method is simpler to implement, and it achieves fast convergence speed.