The equalizer is the central part of the receiver and its performance significantly affects the overall performance of the system in the mobile communication. A proposed equalizer is composed of the channel estimator, MLSE based on the Viterbi algorithm and GMSK decoder. The approximation of GMSK with QPSK has great impact on the equalizer design, because it allows us to use the existing simple and efficient algorithms for designing optimal QPSK equalizer. In order to estimate efficiently channel, we use a sliding window algorithm based on energy calculation and cross-correlator. And also a tuning scheme is presented in order to improve the equalizer performance. Simulation results indicate that a proposed equalizer meets the GSM standards easily in terms of performance.