The optimal design of an extrapolated impulse response (EIR) filter (in the mini-max sense) is a non-linear programming problem. In this paper, the optimal design of the EIR filter by the semi-infinite programming (SIP) is investigated and an iterative technique for optimally designing the EIR filter is proposed. The simulation experiment validates the effectiveness of the SIP technique and the proposed iterative technique in the optimal design of the EIR filter.