The evolutionary history of Palaeozoic and early Mesozoic ray-finned fishes (Actinopterygii) is obscured by an incomplete fossil record and under-study of late Palaeozoic (Permo-Carboniferous) actinopterygians. To help address this issue, we describe a new species of ray-finned fish, Concentrilepis minnekahtaensis gen. et sp. nov., from the late early Permian (Kungurian) Minnekahta Limestone of South Dakota (USA). This taxon is represented by Field Museum of Natural History FMNH PF 3721, an exceptionally well-preserved partial three-dimensional head and trunk preserving the external anatomy and some internal elements from the skull, paired fins and scale cover. Concentrilepis is also represented by Yale Peabody Museum 18649, a laterally compressed individual that preserves the posterior portion of the body. This taxon has features of the paraphyletic ‘paleoniscoids’, including an immobile maxilla with a narrow suborbital process and a broad postorbital expansion, a heterocercal caudal fin, and rhombic ganoid scales. Concentrilepis is distinguished from similar species by the dual lateral expansions on its frontal (= parietal of sarcopterygians), the exclusion of the lacrimal from the oral margin, and lateral scales that are longer than deep and ornamented with straight, concentric ridges at their margins and diagonal ridges at their centres. We conducted a maximum parsimony analysis in PAUP and a Bayesian analysis with the Mkv model in MrBayes with 73 other taxa and 222 characters that placed this taxon in a polytomy with other late Palaeozoic and early Mesozoic ‘paleoniscoids’. We also found that the application of Bayesian and parsimony techniques in tandem provided the necessary caution in interpreting our results and focused direction for future study. Continued efforts to gather more morphological data from ‘paleoniscoids’ in concert with the development and testing of novel phylogenetic characters and inference techniques will be necessary to improve our understanding of the interrelationships of late Palaeozoic and early Mesozoic actinopterygians. http://zoobank.org/urn:lsid:zoobank.org:pub:9F12F99D-A33A-41C2-AC34-F4936786020B