Piers Goodwin, 45, was last seen on Monday night at his home in Edwin Court, Fratton, and was reported missing yesterday morning.
Police said he has not been in contact with family or friends, which is out of character for him and they are understandably growing increasingly concerned.
Piers is white, stocky, 5ft 10ins tall, has light brown spikey hair and a full beard.
He left in his black Mercedes convertible that has a registration plate that ends with WTM, which officers believe was seen in the Wareham area of Dorset yesterday afternoon.
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A police spokesman said: ‘We would ask anyone with friends and family living in that area to share this appeal with them too.
‘Have you seen anyone matching this description? Do you know where he is? Please get in touch.’
Anyone with information should call 101, quoting 44180104874.