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In this paper, a new IIR notch filter with transient suppression is proposed. The proposed algorithm utilizes a varying pole radius to significantly reduce the transient effect when eliminating a sinusoidal interference in signal enhancement. Based on a time-varying linear difference equation, the analytical solution to a sinusoidal interference is found. With a given tolerance of the transient disturbance, a scheme is derived to predict the duration of the transient response and to determine the damping parameter used for changing the pole radius. Computer simulations demonstrate that the developed pole-radius-varying IIR notch filter significantly outperforms the traditional IIR notch filter.