Linear dunes occur on planetary surfaces, including Earth, Mars, and Titan, yet their dynamics are poorly understood. Recent studies of terrestrial linear dunes suggest they migrate by elongation only in supply-limited environments. Here, we investigate elongating linear dunes in the Hellespontus Montes region of Mars which are morphologically similar to terrestrial systems. Multitemporal, high-resolution orbital images show these linear dunes migrate by elongation only and that the fixed sediment source of the dunes probably restricts any lateral migration. Some linear dunes maintain their along-length volume and elongate at rates comparable to adjacent barchans, whereas those which decrease in volume show no elongation, suggesting they are near steady state, matching morphometric predictions. Limited sediment supply may restrict Martian linear dunes to several kilometers, significantly shorter than many terrestrial linear dunes. Our results demonstrate the close similarities in dune dynamics across the two planetary surfaces.