Tucker the tortoise vanished from an insecure greenhouse some time between 10am and 12pm on Friday 18 October 2013.
The female tortoise is thought to be 60 to 70 years old and is said to be worth around £300. She has been micro chipped.
PC Sally Ludlow, of Weymouth police, said: “The owners are devastated by the loss and urge anyone with any information to come forward.
“I have notified local vets and would also like to hear from anyone who may have been offered a tortoise for sale or may have seen one advertised in strange circumstances.”