  We introduce a Z$_3$-graded quantum $(2+1)$-superspace and define
Z$_3$-graded Hopf algebra structure on algebra of functions on the Z$_3$-graded
quantum superspace. We construct a differential calculus on the Z$_3$-graded
quantum superspace, and obtain the corresponding Z$_3$-graded Lie superalgebra.
We also find a new Z$_3$-graded quantum supergroup which is a symmetry group of
this calculus.
