Launched by local resident and lecturer Daryl Tayar, the petition claims that clear-cutting, such as has already been carried out on a stretch by the River Kelvin, "is absolutely contrary to what the public wants" according to Glasgow City Council's own public consultation.
It urges the council to "drop this policy and instead protect the wooded areas in the park for the benefit of park users and wildlife".
The Friends of Kelvingrove Park group promoted the petition on its Facebook page, saying: "Glasgow City Council have been at it again with the chainsaw overkill in Kelvingrove."
But a local authority representative said: "We are not felling the majority of trees as has been suggested. The council has a duty of care to manage the tree cover within its many parks and open spaces and where trees are in terminal decline, a threat to the public or to parks infrastructure, they will be removed."
Created in 1852 by Sir Joseph Paxton, the park is one of four sites in Glasgow listed in Historic Scotland's Inventory of Gardens & Designed Landscapes in Scotland.