This paper proposes a weighted least-squares (WLS) method for designing variable one-dimensional (1-D) FIR digital filters with simultaneously variable magnitude and variable non-integer phase-delay responses. First, the coefficients of a variable FIR filter are represented as the two-dimensional (2-D) polynomials of a pair of spectral parameters; one is for tuning the magnitude response, and the other is for varying its non-integer phase-delay response. Then the optimal coefficients of the 2-D polynomials are found by minimizing the total weighted squared error of the variable frequency response. Finally, it is shown that the resulting variable FIR filter can be implemented in a parallel form, which is suitable for high-speed signal processing.