Summary: Motivated by Chi-Kou’s weighted least-squares (WLS) Chebyshev approximation method for the design of FIR filters with linear phase, we propose a new self-initiated iterative WLS Chebyshev approximation method for the design of FIR digital filters with arbitrary complex frequency response and real filter coefficients. The proposed method not only inherits all the advantages of Chi-Kou’s method but also is computationally more efficient than Chi-Kou’s method for the case of linear phase FIR filter design. On the other hand, contrast to Chit- Mason’s time-domain least mean square (LMS) approximation methods, the proposed method is a frequency-domain WLS method based on similar philosophies. Several design examples are provided to demonstrate the good performance of the proposed method.