Lemvig is a market town on the Limfjord River in North Jutland, Denmark. The town has a population of 6,741 (2025), and is the seat of Lemvig Municipality in the North Jutland Region.

Lemvig lies between the Limfjord and Lemvig Lake (Danish: Lemvig Sø), and is nestled between hills to the east and west. The local topography was shaped during the last ice age. It was settled during the Middle Ages and saw significant expansion during the 19th century as a result of trade.

The town is situated 10 kilometers (6¼ miles) from the North Sea and 375 kilometers (233 mi) from Copenhagen. The town takes its name from the Lem Vig (lit. 'Lem Bay'), a bay on the western part of the Limfjord, and part of Nissum Bredning. The town lies at the interior end of the bay, and originally was settled on a flat strip of land between the fjord and Lemvig Lake (Danish: Lemvig Sø), surrounded to the east and west by steep hills. Gradually, the town has expanded and spread up the sides of the valley.

Until the Agger Tange was breached in 1825, Lemvig was isolated from the north sea, though it was located on the shipping route to Thy within the Limfjord. Facing the Limfjord, the harbor of the town has a 2-meter high concrete seawall to protect the city from westerly storms which push water from the North Sea into the Limfjord.

The oldest record which mentions Lemvig were a series of royal letters from 1234 and 1237 which mention the town of Læmwich and Lemvich. During the Middle Ages, Lemvig remained a small town with only a church. In 1479, a fire destroyed the town hall.

In 1542 King Christian III ordered the establishment a school in the town. Lemvig was designated as a market town, perhaps as early as 1471, but certainly by 1545. By 1638, it was described in priest's reports as "a small market town".

The early modern period saw Lemvig go into a slight decline. In 1672 the town had a population of 450, but by 1769 only had 316. This decline may have been the result of a series of fires, the largest of which in 1684 burned most of the town down. It wasn't until the mid 19th century that Lemvig saw significant expansion, as the opening of the Agger Tange in 1825 and the opening of the Løgstør Canal in the 1850s had brought new opportunities to the town. A new port was constructed in the 1850s to facilitate increased agricultural trade through the Limfjord to Aalborg.

In 1879 the Lemvig railway line was constructed through Lemvig. To save money, its station had been constructed on the plateau above the town, rather than being brought down into the valley itself. This meant that goods from the city needed to be hauled up the steep slopes before being shipped south. With increasing volumes of goods, it became evident that a rail connection directly at the harbour was need, and finished construction in 1892.^{[citation needed]}