This paper analyzes the performance of the GP-NLMS algorithm, revealing the nature of its fast convergence as well as its deficiency of inducing bigger steady state error. Based on the analysis, a class of improved generalized-proportionate stepsize LMS (GPS-LMS) algorithms are proposed. With an efficient switching mechanism, the new algorithms can dynamically switch between the GP-NLMS and conventional LMS-type algorithms to achieve fast initial convergence and tracking speed and low steady state error. Computer simulations verified the superior performance of the proposed algorithms