The presence of noise superimposed on a signal limits the receiver’s ability to correctly identify the intended signal. The principal of adaptive noise cancellation is to acquire an estimation of the unwanted interfering signal and subtract it from the corrupted signal. Noise cancellation operation is controlled adaptively with the target of achieving improved signal to noise ratio. This paper describes the Least Mean Squares (LMS) adaptive filtering algorithm. The algorithm was implemented in Matlab and was tested for noise cancellation in speech signals.