This paper proposes a design method of 2-D variable IIR digital filters with high frequency tuning accuracy. In the proposed method, a parallel complex allpass structure is used as the prototype structure of the 2-D variable digital filters in order to obtain low sensitivity characteristic. Because the proposed 2-D variable digital filter is composed of first-order complex allpass sections connected in parallel, the proposed variable digital filter possesses several advantages such as low sensitivity characteristic in the passband, simple stability monitoring and high parallelism. In order to improve the frequency tuning accuracy of the proposed variable digital filter, each first-order complex allpass section is substituted by a new first-order complex allpass section with low sensitivity characteristic. Moreover, the coefficient sensitivity analysis of a 2-D parallel complex allpass structure is presented. Numerical examples show that the proposed 2-D variable IIR digital filter has high tuning accuracy under the finite coefficient wordlength.