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).

The plant occurs on the South Island of New Zealand, from the Clarence River extending south to Central Otago. It typically grows in sparsely vegetated montane habitats at elevations between 200 and 1,000 m (660 and 3,280 ft). Flowering occurs from November through January, and the flowers are variably white, pink, and red. Similar species include Convolvulus waitaha and C. fracto-saxosa.

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