As a sarcopterygian fish, the extant coelacanth Latimeria has muscular paired fins, different in their skeletal and muscular anatomy from the paired fins of actinopterygians. Although the muscular anatomy of the pectoral and pelvic fins of Latimeria has been described by several studies, a detailed functional description of the muscles and their architecture has never been performed. Our detailed functional description of the muscles of the paired fins shows a more complex organization than previously described. The pectoral and pelvic fins have a different organization of their muscular anatomy, and the pelvic fin shows a more plesiomorphic configuration of the muscles since most of them are poly-articular and run from the pelvic girdle to the fin rays, an organization typical of actinopterygians. We found that the pectoral fins are stronger than the pelvic fins which is likely to be associated with the greater contribution of the pectoral fins to locomotion and manoeuvring. Finally, the study of the joint mobility of the paired fins showed that the pectoral fins show greater mobility than the pelvic fins. The reduced mobility of the pelvic fin is possibly a consequence of the morphology of the mesomeres and the large pre-axial radials.