Estimating the frequencies of a multi-component sinusoidal signal is a fundamental problem in signal processing that has very wide and diverse application areas. Most of these applications require very fast and accurate estimation of the sinusoidal frequencies. This letter presents a fast, accurate, simple, and powerful DFT-based algorithm that estimates the frequencies of sums of multiple exponential sinusoidal signals. We show that the presented algorithm requires much less computational cost compared to conventional parametric and non-parametric methods. The simulation results show that the proposed method nearly reaches the Cramer-Rao lower limit after a certain SNR threshold.