Abstract: In all practical scenarios the extraction of noise free speech signals is an essential task. Many undesired noises are added with the desired speech signal during the transmission. The noises should be eliminated at the destination point. To eliminate the noises the basic widely used type of adaptive algorithm that is Least Mean Square (LMS) algorithm used in several practical applications due to its robustness and simplicity. Step-size is an important parameter in the LMS algorithm. For rapid step size, rate of convergence will be fast, but rise in mean square error (MSE) is main disadvantage. Apart from that, MSE will be small for the smaller step size, but convergence rate will be quit slowly. Hence, step size gives a tradeoff between rate of convergence and MSE. Performance of the algorithm is increased with variable step size parameter. With the variable step size parameter, we developed several variants of LMS algorithm; they are data variable LMS (DVLMS), error variable LMS (EVLMS), time variable LMS (TVLMS) and step variable LMS (SVLMS) algorithms. In these variants, step size is not fixed and it varies based on error signal at a particular instant. With these techniques improves the quality of the signal, the MSE will be decreased and the signal to noise ratio (SNR) also will be improved for speech signal. Several Adaptive noise elimination (ANE) techniques are developed based on these LMS variants and the performance of these ANEs is analyzed, the proposed schemes are well suited for clinical scenarios in speech therapy applications.