Steve Grey (51) travelled from Guernsey to Poole on a planned trip on 27 March.
He had been staying in hotels, but has not been seen or heard from since 8 April.
He is described as white, 5 ft 7 ins tall and of medium build. He has long grey hair and a beard.
Inspector Steve Horton, of Dorset Police, said: ‘For Steve not to have contacted anyone recently or update his social media is completely out of character and I am appealing to anyone who may know his whereabouts to please get in touch.
‘I would also appeal to Steve directly that if he sees this appeal to contact us as we want to ensure you are safe and well.’
Anyone with information is asked to contact Dorset Police at dorset.police.uk, or email 101@dorset.pnn.police.uk.
