A polynomial approximation method is proposed to construct an analytical expression of the boundaries of the damping-ratio-based small-signal security region（D-SSSR） by using the implicit function approach. Because this method gives the explicit polynomial expression， it has broad perspectives in applications. This method establishes the calculation model of the D-SSSR boundary by rotating the coordinate axis of the traditional small-signal security region（SSSR） boundary model. Then， the calculation of the coefficients of the polynomial approximation can be converted into the problem of solving a group of linear equations by using the implicit function approach. Further more， in order to handle the problem of local validity due to the polynomial approximation， an optimization formula is proposed to estimate the credible region of the approximation with a given accuracy. The correctness and effectiveness of the proposed methods are verified through the case studies on IEEE 118-bus system.