| Alexander Peter Cockburn | |
| Riding1: | Ontario North |
| Parliament1: | Canadian |
| Successor1: | Frank Madill |
| Term Start1: | 1882 |
| Term End1: | 1887 |
| Riding2: | Muskoka |
| Parliament2: | Canadian |
| Predecessor2: | Riding created |
| Successor2: | Riding abolished |
| Term Start2: | 1872 |
| Term End2: | 1882 |
| Office3: | Ontario MPP |
| Term Start3: | 1867 |
| Term End3: | 1871 |
| Predecessor3: | Riding established |
| Successor3: | Duncan McRae |
| Constituency3: | Victoria North |
| Birth Date: | 7 April 1837 |
| Birth Place: | Finch, Upper Canada |
| Death Place: | Toronto, Ontario |
| Party: | Liberal |
| Occupation: | Businessman |
Alexander Peter Cockburn (April 7, 1837 - June 2, 1905) was a Canadian businessman and political figure. He represented Victoria North in the 1st Parliament of Ontario and Muskoka and then Ontario North in the House of Commons of Canada as a Liberal member from 1872 to 1887.
He was born in Finch in 1837, the son of Scottish immigrants. He moved to Kirkfield with his family in 1857. He opened a store there in 1863 and became postmaster. He was reeve of Eldon Township from 1864 to 1865. In 1864, he moved to Orillia. After a visit to the Muskoka District in 1865, he moved to Gravenhurst, where he opened a general store, established stagecoach service and initiated steamboat service on Lake Muskoka. In 1867, he helped found the Muskoka Settler's Association and became its first president. While in office, he lobbied for improved rail and water links to the region. Cockburn also published pamphlets describing the natural beauty of the region, aimed at promoting tourism. His steamboat operation expanded to ten ships and a booming resort industry developed in the Muskoka region, that has continued to the present time.
He died in Toronto in 1905.