© 2020 IEEE.A computationally efficient method for the fundamental frequency estimation of a group of harmonically related complex sinusoids is given. To this aim, an efficient frequency estimation method for single tone complex sinusoids is adapted to the harmonic frequency estimation problem. The main idea of suggested Fast Fourier Transform (FFT) based method is the frequency estimation of individual complex sinusoids after the removal of the interference over the tone by other harmonics. After several iterations of estimation and interference cancellation, frequency estimates of each harmonic component are fused to obtain the fundamental frequency estimate. A theoretical study of the suggested scheme and its experimental verification is provided.