  The research on minimal cones over products of spheres is a very important
problem with a long history, many people have contributed to this issue. It was
given a complete answer in \cite{lawlor1991sufficient} by Gary R. Lawlor where
he developed a general method for proving that a cone is area-minimizing, the
so-called Curvature Criterion. In this paper, we generalize the case of
products of spheres to the case of products of embedded Grassmannian manifolds
into spheres where they are similar in many ways, and we give a class of
area-minimizing cones associated with them by using Curvature Criterion.
