Some 1155 boards have options to mount a 775 cooler, as people kept the same cooler when they upgraded from 775 to 1155. However, if the board is 775 and was made prior to the 1155 socket, then I do not believe it will work. On the 1155 boards that allow both, the mounting holes are not in the same spots.
That said, if you can find a 1155 cooler that is listed as universal, like the Cooler Master Hyper 212, then it could possibly work with no problems. http://www.microcenter.com/single_product_results.phtml?product_id=0315397