Frequency estimation is a fundamental problem in many areas. The well-known A&M and its variant estimators have established an estimation framework by iteratively interpolating the discrete Fourier transform (DFT) coefficients. In general, those estimators require two DFT interpolations per iteration, have uneven initial estimation performance against frequencies, and are incompetent for small sample numbers due to low-order approximations involved. Exploiting the iterative estimation framework of A&M, we unprecedentedly introduce the Padé approximation to frequency estimation, unveil some features about the updating function used for refining the estimation in each iteration, and develop a simple closed-form solution to solving the residual estimation error. Extensive simulation results are provided, validating the superiority of the new estimator over the state-the-art estimators in wide ranges of key parameters.