In this paper a new Normalized Least mean square (NLMS) algorithm is proposed by modifying Error-data normalized step-size algorithm (EDNSS). The performance of proposed algorithm is tested for nonstationary signals like speech and Electroencephalogram (EEG). The simulations of above is carried by adding stationary and nonstationary Gaussian noise , with original speech taken from standard IEEE sentence (SP23) of NOIZEUS data base and EEG taken from EEG database (sccn.ucsd.edu). The output of proposed and EDNSS algorithm are measured with excess mean square error (EMSE) in both stationary and non stationary environment. The results can be appreciated that the proposed algorithm gives improved result over EDNSS algorithm and also the speed of convergence is maintained same as other NLMS algorithms.