28 January 2016 Last updated at 14:43 GMT
A controlled explosion was carried out on the vehicle which was parked close to the graves of people who recently died.
It is the third weapon police have recovered in recent days.
A military style assault rifle was found in Strabane last weekend.
BBC News NI's north-west reporter, Keiron Tourish has the details.
There has been anger in Londonderry after two handguns were found in a car in the City Cemetery.