The Fourier algorithm has the ability to filter the integral harmonic and inhibit non-integer harmonics, so it is widely used in electrical power systems for signal analysis. However, the traditional Fourier algorithm is affected by aperiodic components and produces considerable errors. Based on a quantitative analysis of calculation errors that may be caused by aperiodic components, an improved Fourier algorithm is proposed. First, the sampling values of two different power frequency periods are integrated to calculate the aperiodic component parameters, and then we eliminate the errors from the calculation results of the traditional Fourier algorithm. The error calculation method of Taylor series is extended and deduced. By setting the application conditions and optimization measures, the improved Fourier algorithm can ensure both speed and accuracy. Static model signals and Matlab/Simulink simulated signals are used for simulation verification. The results indicate that compared with the traditional Fourier algorithm, the improved Fourier algorithm can effectively eliminate the influence of aperiodic components, and so it has good calculation precision and practicability. This work is supported by the National Natural Science Foundation of China (No. 51777071).