Abstract: The design theory of FIR filter is mostly about the amplitude frequency response performance of passbands and stopbands, which makes the errors between practicality and expectation minimum, such as the one-norm, two-norm and so on. Nonlinear group delay constraint is rarely taken into consideration in most research papers. Therefore, above-mentioned methods can not be applied in the situation of high level with nonlinear group delay constraint. This correspondence presents a new method for equiripple FIR digital filter design with group delay constraint. The main idea of this paper adopts Taylor approximation to transform the original equiripple filter optimal design problem with nonlinear group delay constraint into sequential second-order cone programming framework at the good initial interative point. The problem of group delay constraint could be effectively solved by the proposed method in this paper. Simulations are presented to illustrate the minimal ripple of the passbands and the stopbands, the significant reduction of group delay error and the good performance of the optimal filter design. The final results are consistent with the theoretical analysis. Simulations results also compare the design performance with two methods of SOCP algorithm and Sequential Cone Programming algorithm, and the results verify the usefulness of the algorithm.