The characteristics of industrial environmental noise is analyzed and the adaptive noise cancellation algorithm is applied to the processing of industrial noise. On the basis of traditional least mean square（ LMS）algorithm and variable step size LMS algorithm based on Lorentzian function

the constraint stability condition is further processed. A variable step size LMS algorithm for constrained stability is proposed. In order to verify the effectiveness of the algorithm

simulation is carried out on the Matlab platform. And the result show that the proposed algorithm has faster convergence speed and smaller steady-state error. In addition

the influence of gradient noise on the performance of the algorithm is effectively reduced in this algorithm.