This paper proposes a design method of variable IIR digital filters based on balanced realizations and minimum round-off noise realizations of digital filters. Highly accurate variable digital filters are easily derived by the proposed method. The coefficient matrices of both realizations of second-order digital filters are obtained directly from prototype realizations. The filter coefficients of variable digital filters can be obtained by frequency transformations to the realizations. The filter coefficients are presented as truncated Taylor series for the purpose of reducing a number of calculations to tune the coefficients. However the proposed filters have highly accurate variable characteristics against the coefficient truncation since balanced realizations and minimum round-off noise realizations have very low coefficient sensitivities, which are invariant under the frequency transformations. Moreover, the dynamic ranges of the proposed filters are almost constant against the frequency transformations. Numerical examples show the effectiveness of the variable digital filters designed by the proposed method.