The Joseph Rowntree Housing Trust has applied for planning permission to chop down 41 trees at Homestead Park in Water End.
A spokesman for the trust said the park is “suffering from overcrowded planting” but that more trees could be planted in the future.
He added that the team will work with City of York Council’s tree officer on the plans.
The trust, which runs the park, says 19 of the trees due to be removed are around the main lawn and borders. A further 22 trees are set to be cut down are on edges of the park.
They are mostly conifers, according to planning documents.
A spokesperson for the Joseph Rowntree Housing Trust said: “The management plan for Homestead Park helps us to manage the park and ensure areas of historic importance are protected.
“Recent surveys have highlighted several areas within the park which are suffering from overcrowded planting. This can cause damage to trees which prevents them from developing fully.
“For this reason, we are planning to remove trees in these overcrowded areas. We will be working closely with the tree officer from the City of York Council to agree an approach including the possibility of planting trees in the future.”
Under the plans seven holly trees would also be reduced.
The application says trees that are cut down could be replaced with deciduous trees , which drop their leaves in the autumn.
Others would be removed to allow more light to get through or for the borders to be replanted. Planning permission from City of York Council is required before trees in a conservation area can be cut down.
The 14-acre park was opened in 1904 by social reformer Benjamin Seebohm Rowntree, son of Joseph Rowntree who owned Rowntree’s Chocolate Factory.
Homestead House, within the park, was the home of Seebohm and his family from 1904 to 1936. It is now the head office of the Joseph Rowntree Foundation.