Danny Love, aged 38, from Morley, was reported missing on November 25 after not being heard from for a week.
There are concerns for his welfare.
Enquiries have established the last confirmed sighting of him was in Harrogate on November 21.
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He is described as white, 6ft to 6ft 1in tall, stocky, with brown hair and blue eyes.
His left arm is missing from below the elbow.
He was last seen wearing a dark jacket, red t-shirt, black tracksuit bottoms and a black beanie hat.
Anyone who has seen him or who has any information that could assist in tracing him is asked to contact Leeds South officers via 101 quoting log 889 of November 25 or online via www.westyorkshire.police.uk/101livechat