The primary objective of this paper is to present a simulation scheme to simulate an adaptive filter using Least Mean Square, and Normalized Least Mean Square adaptive filtering algorithms for system identification and echo cancellation. The objective of echo cancellation is to estimate the unknown system response that is system identification. With the help of system identification and adaptive filtering algorithms Mean Square Error (MSE) can be minimized and hence echo free signal can be obtained. This method uses a primary input signal that contains speech signal and a reference input signal containing noise. The estimated signal is obtained by subtracting adaptively filtered reference input signal from the primary input signal. In this method, the desired signal corrupted by an additive echo can be recovered by an adaptive echo canceller using LMS, and NLMS algorithms. This adaptive echo canceller is useful in minimizing the MSE and to improve the SNR. Here the estimation of the adaptive filtering is done using MATLAB environment.