The taxonomic status of the sand fly Phlebotomus (Euphlebotomus) argentipes Annandale & Brunette 1908, which transmits Leishmania (Leishmania) donovani (Laveran & Mesnil 1903) in southern Asia, is reassessed, because variation in morphology, behavior, and distribution suggests it to be a complex of sibling species. The putative complex is composed of the nominotypical member Phlebotomus argentipes sensu stricto, Phlebotomus annandalei Sinton 1923 status revived and Phlebotomus glaucus Mitra & Roy 1953 new status. An allolectotype is designated for the female of P. argentipes as well as neotypes for the males of P. annandalei and P. glaucus. Morphological descriptions, illustrations, and keys are presented to allow identification of adult males and females. Based on female morphological characters, P. argentipes s.s., P. annandalei and P. glaucus can be distinguished from each other using principal component analysis. P. glaucus is widespread in India, occurring sympatrically with P. argentipes s.s. in L. donovani-endemic foci, whereas P. annandeli is peripatric to the type species in Chennai, southern India. “In copula” is a process of postcopulatory sexual selection occurring as correlated coevolution of male and female reproductive traits, which drives species isolation. This pattern has been implicated in reproductive isolation among the members of the P. argentipes complex. Further research on adult behavior and larval biology of the P. argentipes complex is needed to understand the epidemiology and control of visceral leishmaniasis.