In this paper, we propose a new SO-MLSE(soft-output maximum likelihood sequence estimation) equalizer, which can be used in GSM digital cellular system) it uses complex correlation of training sequence to obtain the channel information and the equalization is performed by MLSE using Viterbi algorithm. In order to generate a soft-decision input to channel decoder (Viterbi decoder), the soft-output equalization algorithm is needed. The adopted algorithm doesn't require to modify the structure of HO-MLSE(hard output MLSE) equalizer, that is, SO-MLSE equalizer can be implemented by adding soft-output generation block to HO-MLSE equalizer. This algorithm uses the outputs of matched filter and HO-MLSE equalizer. It turns out that the complexity of proposed SO-MLSE equalizer is simpler than those of other SO-MLSE equalizer and its perforance is almost the same as those of others. Finally, the proposed SO-MLSE equalizer is also implemented s a prototype with ADSP-2101 16-bits fixed point digital signal processing chip.