In the paper, an echo canceller is discussed which is based on system identification approach. This canceller uses some adaptive algorithms such as Least Mean Square Algorithm & an Improved LMS algorithm, which also called as the Fractional Least Mean square algorithm. The algorithms use FIR filters with taps, which are chosen to minimize the error signal coming from the system, where minimization of the error based on the stochastic gradient method. Both algorithms such as LMS & FLMS are discussed & simulated in Mat lab. The echo is generated in Mat lab by adding several delayed and attenuated replica of speech. The comparison in between the algorithms was discussed on the basis of their convergence rate.