Odonatans are quite rare in the fossil record compared with the other insects, especially in Cretaceous amber inclusions. The extant family Platystictidae is one of the most diverse Zygoptera, but short of fossil records. In this paper, a new species, Mesosticta davidattenboroughi sp. nov., is described from mid-Cretaceous Burmese amber, representing the third-known fossil species of Platystictidae. Mesosticta davidattenboroughi sp. nov. has a long IR1 beginning one cell distal of the base of RP2, confirming the previous attribution of Mesosticta Huang, Azar, Cai & Nel, 2015 to Platystictidae. It differs from other species of Mesosticta in having a long IR1 and a basally crossed subdiscoidal cell. The fossil genus Mesosticta shares the diagnostic characters of the modern platystictid genera, viz. a basally recessed 'CuP' (shared by all species), a very long IR1 (only in Mesosticta davidattenboroughi sp. nov.), and a specialized subdiscoidal area mostly rhomboidal in shape (only in Mesosticta electronica Zheng, Zhang, Chang & Wang, 2016). Based on the platystictid damselflies from Burmese amber, a new subfamily Mesostictinae subfam. nov. is established. Mesostictinae subfam. nov. represents the first fossil group of modern platystictid damselflies, documenting the appearance of Platystictidae as early as mid-Cretaceous. It differs from modern Platystictidae by the presence of fewer postnodal and postsubnodal crossveins, a short MP, the base of RP2 being nearer to the subnodus and the nodus lying more distally.