This paper develops a new algorithm based on the Projected Gradient Algorithm (PGA) for the design of FIR digital filters with “sum of power of two” coefficients. It is shown that the integer programming involved in the FIR filter design can be solved by this algorithm. It is compared with the reported method for a SemiDefinite Programming (SDP) relaxation- based design. The simulations demonstrate that the new algorithm often yields the similar error performances of the FIR filter design, but the average CPU time of this approach is significantly reduced. This paper develops a new algorithm based on the Projected Gradient Algorithm (PGA) for the design of FIR digital filters with “sum of power of two ” coefficients. It is shown that the integer programming involved in the FIR filter design can be solved The simulations demonstrate that the new algorithm often yields the similar error performances of the FIR filter design, but the average CPU time of this approach is significantly reduced.