Elimination of tainted noise and improving the overall quality of a speech signal is speech enhancement. To gain the advantage of individual algorithms we propose a new linear model and that is in the form of cascade adaptive filters for suppression of non-stationary noise. We have successfully deployed NLMS (Normalized Least Mean Square) algorithm, Sign LMS (Least Mean Square) and RLS (Recursive Least Square) as the main de-noising algorithms. Moreover, we are successful in demonstrating that the prior information about the noise is not required otherwise it would have been difficult to estimate for fast-varying noise in non-stationary environment. This approach estimates clean speech by recognizing the long segments of the clean speech as one whole unit. During experiment/implementation we used in-house database (includes various types of non stationary noise) for speech enhancement and proposed model results have shown improvement over conventional algorithms not only in objective but in subjective evaluations as well. Simulations present good results with a new linear model that are compared with individual algorithm results.