In this thesis, active noise control of symmetric α stable (SαS) distribution impulsive noise has been studied. Two kinds of algorithm based on Sigmoid transformation of error signal have been proposed. The convergence condition of algorithms also has been analyzed. It does not need the parameter selection and thresholds estimation. Computer simulations were carried out to validate algorithm. Simulation results have proven the effectiveness of the algorithm and achieved the expected control effect. Compared to the previous algorithm, the convergence speed is improved.