This paper discusses about some algorithms of variable step size LMS adaptive filtering and establishes another new non-linear functional relationship between μ and

e(n)

.The functional relationship is not only simpler than Sigmoid functional relationship

but also has the property of slight change

e(n)

near to zero.Therefore it is superior to Sigmoid functional relationship in the process of step size change of adaptive steady state.On the basis of the functional relationship

The author presents the new algorithm of variable step size LMS adaptive filtering and analyses the algorithm with various α and β.the algorithm has less computational complexity than the former algorithms

besides good convergence properties.Computer simulation results confirms the theoretical analysis and shows the algorithm performance is bett

er than that of former algorithms.