In this paper, we propose a complex-valued IIR filter for digital VSB signals based on CMA in order to efficiently mitigate multipath distortions, especially the leakage from the quadrature component. The proposed equalizer overcomes the drawback of the conventional real-valued IIR equalizers that it attempts to equalize Hilbert transform of quadrature component. We demonstrate via simulation that the proposed complex IIR filter successfully mitigates the leakages from the quadrature component, while the conventional real IIR filter requires a longer IIR filter to achieve the same performance. We present cost function analysis for a simple two-tap case showing that the proposed IIR equalizer with CMA for VSB signals has a global minimum at the desired location.