A new adaptive filtering algorithm is proposed in this paper.The proposed algorithm is of simple structure

medium computational complexity and fast convergence

and makes up for the defects that general LMS algorithm is of less computational complexity but of slow convergence and the Affine Projection Algorithm (APA) is of fast convergence but of large computational complexity.The structure of the new algorithm is much simpler than APA and its improved version

but it has the same convergence as APA.We not only analyses its performance but also succeed to apply it to multi-channel echo cancellation.Simulation in MATLAB shows its computational complexity is much lower than Sankaran's(1997) and Benesty's(1996) but they have the same convergence and accuracy.Hence it has better tracking ability.