The grey Land Rover DEF 110XS Utility was parked on a driveway in St John while the owners were away from 15 to 25 May.
While they were gone, thieves stole an Expedition roof rack, rear ladder, ribbed aluminium under-shield, foot step and rear step bumper.
The police have asked Islanders to be on the lookout, and to come forward if anyone has been offered the parts for sale.
Anyone with any information should contact the police on 612612 or on the anonymous Crimestoppers number 0800 555111.