We presents a squared sine functioned adaptive (SSA) algorithm for acoustic-echo-cancellation (AEC) applications in-presence-of impulsive noise. In the development of the SSA algorithm, a novel cost function is constructed by exerting a sliding window type squared sine function on the estimation error vector, which provides robustness in the impulsive-noise environments and speed-ups convergence when the input is colored signals. Theoretical models for predicting the mean-weightbehavior, transient excess-mean-square-error (EMSE) behavior, and tracking behavior are presented. Moreover, the optimal step size and minimum EMSE of the tracking performance are provided. The computation complexity of SSA algorithm has also been investigated. Numerical experiments demonstrate that the theoretical results match well with simulation results and show the superiority of the proposed SSA algorithm against known algorithms in AEC applications