The victim was found by a member of the public who was walking on the pedestrian walkway behind Thorntreeside, near Easter Road, at around 11.20pm on Sunday when she found the male lying on the ground.
The 41-year-old was taken to the ERI where he remains in a serious condition.
Officers believe the man was robbed of his possessions and are appealing for anyone with information to get in touch.
Detective Constable Andy Cory from Gayfield CID said: “The victim has sustained serious head injuries during the incident and we are now looking to establish what exactly happened and who was involved.
“Anyone who remembers seeing any suspicious activity in the Easter Road area prior to 11.20pm on Sunday evening is asked to contact police immediately.
“We would also urge anyone with any further information relevant to this investigation to also get in touch.”
Anyone with information should contact police on 101.