The aim of this study was to improve the performance of Least Mean Square (LMS) adaptive algorithm used for fading channel estimation. One step Least Square prediction, based on the estimate of the sampled impulse response and the estimate of their speed of variation, is used along with LMS. The efficiency of the algorithm is confirmed by simulation results for slow, moderate and fast varying mobile channel. The results show about 3 to 11 dB improvement in the Mean Square Deviation between the estimated taps and the actual ones depending on the speed of channel time variations. Pedestrian, slow and fast Vehicular channels with doppler frequencies 6, 100 and 222 Hz, respectively, are used in these tests.