The main purpose of this thesis is about a frequency Double-talk detection combined with the GMDF adaptive filter processed the acoustic echo problem in hands free communication system. The proposed Double-talk detector in time domain and frequency domain include a near-end speech detector and an auxiliary filter two kinds of structure. Among them have the best result with the Double-talk detection in the frequency domain. The detector used L subfilters that show extremely tight and severe to differentiate between double talk and single talk. Therefore, this detection differentiated between echo and near-end speech efficiently. This thesis also presents some methods observed convergence characteristic of adaptive filter in time-variant systems.