Rear Admiral James Horsford Cockburn (1817 – 10 February 1872) was a Royal Navy officer who became Commander-in-Chief, East Indies Station.

Cockburn joined the Royal Navy in 1829.

[1] He was appointed Commander-in-Chief, East Indies Station in 1870.

[1] He died in that office while travelling from Trincomalee to Calcutta in 1872.

[1] In 1852 he married Harriet Emily Gedge; they had one son and seven daughters.