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Motif mining is a classical data mining problem which aims to extract relevant information and discover knowledge from voluminous datasets in a variety of domains. Specifically, for the temporal data containing real numbers, it is formulated as time series motif mining (TSMM) problem. If the input is alphabetical and edit-distance is considered, this is called Edit-distance Motif Search (EMS). In EMS, the problem of interest is to find a pattern of length l which occurs with an edit-distance of at most d in each of the input sequences. There exist some algorithms proposed in the literature to solve EMS problem. However, in terms of challenging instances and large datasets, they are still not efficient. In this paper, EMS3, a motif mining algorithm, that advances the state-of-the-art EMS solvers by exploiting the idea of projection is proposed. Solid theoretical analyses and extensive experiments on commonly used benchmark datasets show that EMS3 is efficient and outperforms the existing state-of-the-art algorithm (EMS2).