Convolvulus verecundus, commonly known as trailing bindweed or tussock bindweed, is a species of low-growing flowering plant in the family Convolvulaceae. Endemic to New Zealand, it was formally described as a new species by botanist Harry Allan in his 1961 work Flora of New Zealand. The type was collected near Lake Tekapo in the gorge of the Cass River, at an elevation of 850 m (2,790 ft).