We present a method for estimating the vocal-tract area function from specified formant frequencies. The method extends the work of Story (J.A.S.A., 119, 715-718, 1996) based on a sensitivity function representing the change in the formant frequency due to a small perturbation of the cross-sectional area of the vocal tract. Our method estimates the vocal-tract shape through an iterative procedure in which the sensitivity function is used as the basis function to gradually optimize the cross-sectional area that produces the target formant frequencies. In addition, the summing weight of sensitivity functions is determined by minimizing an objective function representing the relative frequency error of every format. We conducted numerical experiments using area function data of English vowels. Results showed that our method can estimate the vocal-tract shape with satisfactory accuracy. In addition, the number of iterative calculations is significantly lower than with Story's original method.