  We explore the constant curvature holomorphic solutions of the supersymmetric
grassmannian sigma model $G(M,N)$ using in particular the gauge invariance of
the model. Supersymmetric invariant solutions are constructed via generalizing
a known result for ${C}P^{N-1}$. We show that some other such solutions also
exist. Indeed, considering the simplest case of $G(2,N)$ model, we give
necessary and sufficient conditions for getting the constant curvature
holomorphic solutions. Since, all the constant curvature holomorphic solutions
of the bosonic $G(2,4)$ $\sigma$-model are known, we treat this example in
detail.
