Hugh Primrose Lindsay (31 October 1765 – 23 April 1844) was a British naval captain, Chairman of the East India Company and Member of Parliament.
He joined the Royal Navy in 1779 and was promoted to lieutenant in 1782, but by 1787 had left the navy to join the British East India Company's (EIC) marine service, where he was promoted captain in 1793.
He was succeeded, after the death of his wife, by his son Hugh Hamilton Lindsay.
The EIC launched and named a paddle steamer for him: HCS Hugh Lindsay (1829).
This article about a Member of the Parliament of the United Kingdom (since 1801), for a Scottish constituency is a stub.