Emergency services were called to Gorgie/Dalry Community Park in Edinburgh at around 2am on Thursday.
The Scottish Ambulance Service attended but the 48-year-old was pronounced dead at the scene.
Police Scotland has arrested a 50-year-old man in connection with his death.
An area of the Grassmarket has been cordoned off since 2.45am on Wednesday while officers carry out an evidential search as part of the enquiry.
A spokesman said: “Police in Edinburgh are investigating after a man was found with serious injuries in the wooded area at the Gorgie/Dalry Community Park, behind the Lidl supermarket, at around 2am on Thursday.
“The Scottish Ambulance Service also attended and pronounced the 48-year-old dead at the scene.
“A 50-year-old man has been arrested in connection with this incident and inquiries are continuing.”
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