One of the main problems when picking signal so weak as electrocardiogram (ECG), there are several kinds of noise that can affect the ECG such as the power line interference noise (PLIN), muscle contraction noise (MCN), base line drift noise (BLDN), motion artifact noise (MAN), electrode contact noise (ECN), and Gaussian noise. Different filter structures are presented to eliminate these diverse forms of noise sources and their performance. Implement the adaptive Finite Impulse Response (FIR) filters, non adaptive Infinite Impulse Response (IIR) digital filters, and non adaptive Finite Impulse Response (FIR) digital filters to eliminate the above kinds of noise are done. Testing their desired specification using the MATLAB package (version 6.5) in writing the programming code of the simulated system. This system consists of the following: The ECG signal was obtained, and implies the addition of the above six types of noise to the ECG signal, and then filtering process is obtained using the adaptive FIR filters with implementing the Least Mean Square (LMS) algorithm, the non adaptive filters, IIR Butterworth (BW) notch, high pass, low pass filters and the FIR notch, high pass, low pass filters with Hamming window, and Kaiser window.Finally, the adaptive filtering results are the removal of (BLDN, MAN, ECN, and composite noise), and by using the non adaptive (IIR, and FIR) filters, the (PLIN, and MCN) are removed.