A functional link network with higher order statistics is introduced for signal enhancement. The proposed scheme uses the mean-square error (MSE) between higher order statistics of desired signals and filtered output as the learning criterion for training weights in the functional link network. This is motivated by the fact that higher order statistics have a natural tolerance to Gaussian and symmetrically distributed non-Gaussian noises. Results show that the performance of functional link network with higher order statistics is less sensitive to the selection of learning rates than the conventional functional link network and adaptive line enhancement. It is also demonstrated that it can enhance signal more effectively under different noise levels for stationary and nonstationary Gaussian noises.