This paper presents an adaptive MLSE (Maximum Likelihood Sequence Estimator) suitable for TDMA cellular systems. The proposed MLSE has two special features such as handling wide dynamic range signals without analogue gain controls and fast channel tracking capability. In order to handle wide dynamic range signals without conventional AGCs (Automatic Gain Controller), the proposed MLSE uses envelope components of received signals obtained from a non-linear log-amplifier module which has wide log-linear gain characteristics. By using digital signal processing technique, the log-converted envelope components are normalized and converted to linear values which conventional adaptive MLSEs can handle. As a channel tracking algorithm of the channel estimator, the proposed MLSE adopts a QT-LMS (Quick-Tracking Least Mean Square) algorithm, which is obtained by modifying LMS algorithm to enable a faster tracking capability. The algorithm has a fast tracking capability with low complexity and is suitable for implementation in a fixed-point digital signal processor. The performances of the MLSE have been evaluated through experiments in TDMA cellular environments with π/4-shifted QPSK, 24.3k symbol/sec. It is shown that, under conditions of 65dB amplitude variations and 80Hz Doppler frequency, the MLSE successfully achieves less than 3% B.E.R., which is required for digital cellular systems.