  We generalize the monomorphism category from quiver (with monomial relations)
to arbitrary finite dimensional algebras by a homological definition. Given two
finite dimension algebras $A$ and $B$, we use the special monomorphism category
Mon(B, A-Gproj) to describe some Gorenstein projective bimodules over the
tensor product of $A$ and $B$. If one of the two algebras is Gorenstein, we
give a sufficient and necessary condition for Mon(B, A-Gproj) being the
category of all Gorenstein projective bimodules. In addition, If both $A$ and
$B$ are Gorenstein, we can describe the category of all Gorenstein projective
bimodules via filtration categories. Similarly, in this case, we get the same
result for infinitely generated Gorenstein projective bimodules.
