This paper proposes a realization method of high accuracy 2-D variable IIR digital filters with real coefficients. The proposed method uses the reduced-dimensional decomposition form as a prototype structure of 2-D variable digital filters to suppress the degradation of tuning accuracy due to the linear approximation of variable coefficients. Furthermore, the 1-D subfilters of the prototype filter are realized as cascade connections of low sensitivity second-order variable sections to suppress the degradation of tuning accuracy due to finite coefficient wordlength. Numerical examples show that the proposed 2-D variable digital filter has high frequency tuning accuracy under finite coefficient wordlength and the linear approximation.