The B678 was a short link road in Grantham town centre.
It started on the A1 (now A52) London Road and headed west along Wharf Road. After crossing the A607 Harlaxton Road it continued on to end at the wharf on the Grantham Canal (now filled in).
Owing to the short length of the road its history is not completely certain. The road seems to have survived the closure of the canal wharf in the 1930s and indeed the full length of the road is still given Class II status in the 1990s, long after the construction of the A1 Grantham bypass technically put the road out of zone.
The majority of the ex-B678 is now the mainline of the A52 but the section west of the A607 to the wharf is now unclassified.