The vandals have struck twice in a month, causing significant damage at both Newmillerdam and Anglers Country Park.
A bird hide at Anglers was burnt down last week, leaving only the stone part of its structure remaining.
And this attack follows another deliberate fire at Newmillerdam last month, which completely destroyed a picnic bench and damaged part of the Lawns Park boardwalk.
The Friends of Newmillerdam Country Park repaired the walk and a new picnic bench is being ordered, but the cost of the materials is more than £1,000.
Coun Maureen Cummings, Wakefield Council’s cabinet member for environment and communities, said: “We are absolutely disgusted by the anti-social behaviour that has been taking place in our parks.
"These deliberate and deplorable acts of vandalism have caused lasting damage to our fabulous open spaces, destroying local wildlife and spoiling the parks for visitors.
"Our parks are fantastic places to visit and it is shocking that anyone would cause such damage."
West Yorkshire Fire and Rescue Service have already been called out to three fires a Newmillerdam this year.
Mussarat Suleman, Wakefield district prevention manager at the fire service, said: “This year alone we have attended numerous incidents at the park as a result of anti-social behaviour.
"We have seen damage caused to decking, trees and woodland and a fishing platform. It is concerning to see the damage that is being caused to both nature and the wildlife in the area.
“Parks should be safe and pleasant places for visitors to use. I would urge all visitors to remain vigilant at all times, adhere to the instructions provided and report any suspicious activity to the police immediately.”
A much larger fire was deliberately started at Newmillerdam last year, completely destroying the boardwalk and viewing platform.
Its ferocity meant nine trees had to be cut down due to damage and the Friends group rebuilt the items at a cost of £6,000.
Earlier this year, a fishing platform funded and installed by Wakefield Angling Club was also destroyed by fire.
Anyone with information about the recent fires is urged to contact police by calling 101.
And anyone who witnesses signs of a fire in any of the council’s country parks is asked to report it by calling 0345 8 506 506.