An efficient procedure for frequency estimation is proposed in this paper to alleviate the computational complexity. Grounded on the fact that the frequency of a target signal usually lies in a known range in practical applications, two fundamental steps in the frequency estimation, i.e., the discrete Fourier transform (DFT) and the interpolation of the DFT samples, are modified accordingly. Unlike the previous works focusing on either the DFT or the interpolation, this paper does not decouple the two steps but optimizes the whole procedure comprehensively by considering the interrelationship between the two steps. As a result, the number of operations required for the estimation is remarkably diminished while the performance remains competitive with the recent works.