This paper presents a new realization method of variable low-pass infinite impulse response (IIR) digital filters with high tuning accuracy. We construct the proposed variable filters by using the state-space-based frequency transformation proposed by Mullis and Roberts. Since this transformation requires an inverse matrix that leads to high computational cost, we present a new simple algorithm that obtains this inverse matrix by using the step responses of a simple state-space system. This approach imposes no restrictions on the tuning parameter, and thus the cutoff frequencies of the proposed variable filters can be tuned arbitrarily. Furthermore, we show that the proposed variable filters exhibit high tuning accuracy with respect to quantization effects over the entire tuning range.