A new species of the alpheid genus Alpheus Fabricius, 1798, Alpheus sulcipalma sp. nov., is described and illustrated based on the specimens collected from the intertidal zone of Agatti Island, Lakshadweep, India at 0.5-1.0 m depth. This species belongs to the A. edwardsii group by absences of tooth in the orbital hoods and presence of compressed major chela with dorsal and ventral notches. Alpheus sulcipalma sp. nov. is morphologically closely related with A. pacificus Dana, 1852, absence of balaeniceps crests in the minor chela and absences of spine in the merus of major pereiopod of both sexes. However, the new species differs from A. pacificus in presence of strong and broad triangular groove on the dorsolateral and dorsomesial surface of the palm of major chela; length ratio and armature of fingers and palm of minor chela, carpus segments of second and third pereiopods and telson length. The results of phylogenetic analyses using partial sequences of mitochondrial COI gene data compared between A. sulcipalma sp. nov. with congener species which strongly support the description of new species with available limited sequences. The interspecific genetic divergences of the COI gene for A. sulcipalma sp. nov. and A. pacificus were observed higher in ranges (11.1-28.9%).