Abstract An adaptive nonlinear neuro-controller with an integrated evaluation algorithm for nonlinear active noise control systems is proposed to attenuate the nonlinear and non-Gaussian noises. Inspired by the structure of the Hammerstein or Wiener model, the proposed controller is realized by the static nonlinear memory function mapping on the basis of a single neuron. A generalized filtered-X gradient descent algorithm based on an integrated evaluation criterion is developed to adaptively adjust the weights of the controller, where the weighted sum of Renyi's quadratic error entropy and the mean square error is applied as the integrated performance index, which improves the performance of the adaptive algorithm by introducing the information entropy. In addition, the convergence of the proposed approach is analyzed, and the computational complexity among different methods is investigated. The proposed scheme can effectively attenuate the nonlinear and non-Gaussian noises and has a relative simple structure and less learning parameters. The simulation results demonstrate the validity of the proposed method for attenuating the nonlinear and non-Gaussian noises.