Veronica plebeia, commonly known as creeping- or trailing speedwell, is a plant belonging to the family Plantaginaceae native to Australia and New Zealand. Robert Brown described the trailing speedwell in 1810 in his work Prodromus Florae Novae Hollandiae et Insulae Van Diemen. He had collected the species near Sydney in May 1802. A 2012 molecular study found it was most closely related to V. grosseserrata. The flowers are thought to be pollinated by native bees and flies.