Based on the analysis of the ability to extract fundamental wave and the response time delay characteristics of narrow-band filtering algorithm, and combined with the filtering performance of orthogonal filter algorithm, a fast narrow-band filtering algorithm based on orthogonal filter functions is proposed to extract the fundamental component. Two trigonometric functions related with the length of data window are adopted as orthogonal filter functions, and the real and imaginary parts of phasors in their different data window lengths are obtained. The calculation formula of narrow-band filter initial value in each data window length is derived, thereby seeking the initial value of narrow-band filter to shorten the response time delay. The filtering algorithm has good filtering effect and fast response time, and can greatly improve the rapidity of electrical protection and control systems. This work is supported by National Natural Science Youth Foundation of China (No. 51307059) and Fundamental Research Funds for the Central Universities (No. 2016MS90).