Police say the same vehicle has been seen nearby at the time when a number of car thefts took place.
There have been several incidents involving the theft of vehicles in the rural area to the north of Grantham, some of which have been taken with the keys left in the vehicle for just a few moments.
A black Subaru Forester, year 2000 to 2004, has been seen in the area at similar times to thefts. A vehicle registration has not yet been obtained. The vehicle has also been noticed near a number of farms.
Anybody who sees a similar vehicle in the rural areas surrounding Grantham, particularly to the north towards the Newark area, is asked to call police on 101.