Correia Fernandes (2016) described the new genus Grammedessa comprising twelve species. Da Silva Fernandes (2021) described the new genus Calcatedessa including four species and conducted its morphological cladistic analysis associated with all the species of the sister genus Grammedessa including six other new species not yet described. We describe in this paper these six new species: G. fundicava sp.n., G. graciligramma sp.n., G. acalyptoprocta sp.n., G. stichtocephala sp.n., G. nigricava sp.n. and G. longispina sp.n. Also, the female of G. brunneotarsata Correia Fernandes, 2016 is described, and the redescription of G. hamata (Walker, 1868) (transferred from genus Edessa) is presented. The diagnosis, description, and identification key to the species of Grammedessa have been updated, and the distribution of Grammedessa has been extended to Suriname and two other Brazilian states: Maranho and Rondnia.