This paper deals with a state-space approach for adaptive second-order IIR notch filters with constrained poles and zeros. A simplified adaptive iterative algorithm is derived from the gradient-descent method for minimizing the mean-squared output error of an adaptive notch filter. Stability and parameter estimation bias are analyzed for the adaptive iterative algorithm. A numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive state-space notch filter and parameter-estimation bias analysis.