This is the latest phase of the Central Scotland Green Network (CSGN) Development Fund, launchedby Environment Minister Aileen McLeod.
Dr McLeod made the announcement during a tour of the innovative Castlemilk Woodlands Project in Glasgow, which has previously received support from the fund.
She said: "Being able to access high quality greenspace can improve the health, wellbeing and confidence of people and communities. And, as Europe's biggest greenspace project, the CSGN has already made a massive difference to the lives of thousands of people in the central belt.
"I am pleased to be able to invite applications for this latest phase of funding, for projects which will continue the transformation of the central belt into a better place to live, work and visit."
The CSGN Development Fund is managed by the Central Scotland Green Network Trust, with funding provided by Forestry Commission Scotland, Scottish Natural Heritage, Transport Scotland and the Scottish Government. Support is available for feasibility projects as well as physical projects.
Over the past six years, the CSGN Development Fund has supported over 150 projects with £5.8 million.
Keith Geddes, chair of the Central Scotland Green Network Trust, said projects that qualify for funding could include "projects that deliver or lead to woodland enhancement, especially for community use, local food growing initiatives which will engage the community and encourage healthy eating or projects aiming to improve or create access routes to support active travel".
The closing date for applications to the CSGN Development Fund is 18 January 2016. See www.centralscotlandgreennetwork.org for more information.