Law's choice of weapon is a large version of the typical Japanese sword type known as nodachi.
He appears to be quite skilled with it, being able to slice up targets from a distance (although this effect is attributed to his Devil Fruit power).

It is a large sword with an oblong-shaped hand-guard coated with short white fur, sheathed in a black scabbard decorated by white crosses from the opening to the bottom, and with a small piece of red rope tied near its opening.

Due to its size, Law usually carries this sword over his shoulder (in contrast to the other sword-wielding characters in the series, who either carry theirs on their hips or over their backs); yet in other times, he delegates one of his crewmates (namely Bepo) to carry this sword for him.

Name: One Piece Trafalgar Law Black Sword Cosplay Wooden Weapons
(銉兂銉斻兗銈规銇绉戝尰銉堛儵銉曘偂銉偓銉?銉兗銈炽偣銉椼儸鏈ㄥ垁)

Product Material: Wooden
Size: Length 100cm, 4.5cm wide, 4.5cm high