The calculation load of the traditional narrowband active noise control (ANC) system is positively correlated with the number of narrowband frequencies. Its convergence speed and noise reduction effect have the trade-off relationship. To solve the aforementioned problems, this article firstly simplifies the narrowband ANC model based on the filtered-error technology, which makes the system calculation independent of the number of narrowband frequencies. Then, an adaptive mixture parameter combines two simplified narrowband ANC systems to make up a parallel convex combination structure. One system has the fastest convergence speed, and the other system has lower steady-state error. It not only reduces the computational complexity of the traditional narrowband ANC system, but also improves its convergence speed without sacrificing noise reduction result. Experimental results show that the proposed system shortens the convergence time by 78% without sacrificing the steady-state error, which effectively improves the system convergence performance.