A dual fitting algorithm (DFA) for modal parameters identification is presented. The method is implemented in three steps: first, the coefficients of the Forsythe orthogonal polynomials for the rational fraction of the frequency response functions (FRFs) are obtained by fitting the experimental FRF data; then the coefficients of the orthogonal polynomials are converted into the coefficients of ordinary power polynomials by the fitting method again; and finally, the poles and residues of the rational fraction of FRFs in ordinary power polynomials are extracted to identify the modal parameters. Some notes to the definition and use of the recurrence formulation for the real half-function Forsythe orthogonal polynomials are introduced. An example is given to show the aspects of the present method.