  In this paper, we introduce `Pl\"{u}cker weight vector' and establish the
definition of a weighted Grassmann orbifold $\mbox{Gr}_{\mathbf{b}}(k,n)$,
corresponding to a Pl\"{u}cker weight vector `$\mathbf{b}$'. We achieve an
explicit classification of weighted Grassmann orbifolds up to certain
homeomorphism in terms of the Pl\"{u}cker weight vectors. We study the integral
cohomology of $\mbox{Gr}_{\bf b}(k,n)$ and provide some sufficient conditions
such that the integral cohomology of $\mbox{Gr}_{\bf b}(k,n)$ has no torsion.
We describe the integral equivariant cohomology ring of divisive weighted
Grassmann orbifolds and compute all the equivariant structure constants with
integer coefficients. Eminently, we compute the integral cohomology rings of
divisive weighted Grassmann orbifolds explicitly.
