<p>Lungfishes are commonly considered to be the sister group to tetrapods. They appeared around 415 million years ago, then rapidly evolved, diversified and spread. Although many morphological characteristics have remained unchanged over the course of their evolution, their skeleton has evolved considerably towards reduced mineralisation. In particular, their fin skeleton has lost ossification in modern forms. In order to study this process of mineralisation loss, we examined the histology of the pectoral fin mesomeres of <i>Glyptolepis groenlandica</i>. This taxon, as a member of the Porolepiformes – i.e. the most rootward clade in the stem group of lungfish – is important for shedding light on the early evolution of the lungfish postcranial skeleton. Here we show that the central core of each mesomere of the pectoral fin of <i>G. groenlandica</i> remains cartilaginous. We hypothesise that the formation of a primary ossification centre is prevented in the skeletal elements of the pectoral fin of <i>G. groenlandica</i>. Instead, the mineralisation process displays a remarkable combination of ossification patterns. Endochondral ossification results from two processes: (1) in the diaphysis of each mesomere, the formation of connective vascular buds from the perichondrium induces endochondral ossification, as seen only in long bones of modern anurans and in the pectoral and pelvic girdles of extant coelacanths; and (2) in the metaphyses, the endochondral ossification replaces the cartilaginous matrix surrounding chondrocyte columns, as seen in early tetrapods and modern amniotes. Because of the basal position of <i>G. groenlandica</i>, our study likely illustrates the primitive state of fin ossification in lungfish and provides a reference point for understanding the steps that led to mineralisation loss in modern lungfishes.</p>