The Fourier algorithm, due to its good frequency response characteristics, is frequently used in calculating the peak value of a distorted wave for real time measuring applications. A new method, using the linear modulation method, is proposed to implement the algorithm. It improves the defect of a large number of arithmatic operations during implementation of the algorithm. This paper describes the structure and theory of the proposed linear modulated Fourier algorithm. Test results, including the required arithmatic operations and the numerical accuracy, are reported. Moreover, application to the digital impedance relay was simulated, and the simulation results show that the proposed algorithm is suitable for relaying applications.