The Doppler spread, or evenly, the mobile speed of motion, is an evaluation of the spectral spreading of mobile fading channel. A precise estimation of the mobile speed and/or velocity is of great significance in wireless mobile applications which needs the acquaintance of the rate of the channel variations. In this article we propose the use of the auto-correlation of the in-phase component of the received signal to estimate the maximum Doppler shift of the mobile communication system. The proposed algorithm relies on the zero crossing point of the auto-correlation function of the in-phase part of the received signal. A comparison between our proposed algorithm and the algorithm proposed by Tevfik Yucek in term of the Normalized Mean Square Error has been shown.