In this paper, we present a new structure for complex adaptive IIR notch filter which is useful for the detection of complex sinusoids in communication and radar systems. The proposed structure is based on the direct form first-order complex notch filter using gradient-based algorithm. A quantitative analysis for convergence properties is developed. It has been shown that the convergence speed does not depend on the variance of input white noise. The effects of colored Gaussian noise to convergence speed have been analyzed. By using the proposed first-order section, a new cascaded structure for complex adaptive notch filter has been shown. The results of computer simulation are shown which confirm the theoretical prediction.