Dean Conner, 37, was last seen in the Links Avenue area of Musselburgh at about 5pm on Friday December 31 walking towards the Promenade area of the town.
The 37-year-old from Musselburgh is described as 5ft 10in, with short dark brown/black hair and when last seen he was wearing a black hooded top, black jogging bottoms and white trainers.
His mother, Lorraine, is also appealing for information and said: “I am worried sick and need to know that Dean is safe. Dean, please call me or reach out to someone and let them know you are safe.”
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East Lothian Police Sergeant Murray Legge said: “As time passes Dean’s family grow increasingly concerned for him.
“We have carried out a number of enquiries and now have CCTV footage of him, so we know what he was wearing shortly before he went missing.
“We believe that he could have travelled out of the area and would appeal for anyone in Edinburgh, or further afield to look out for him.
“He is likely to travel on foot or by bus. If you know Dean, we want to speak to you – think back, when was the last time you heard from him?
“We urge anyone with any information to come forward.”
Anyone with any information of Mr Conner’s whereabouts is asked to call police on 101, quoting incident number 2238 of Friday December 31.