  We construct (0,2), D=2 gauged linear sigma model on a supermanifold in both
the Abelian gauge group and the non-Abelian gauge group. The $\hat{U}$ operator
provides consistency conditions for satisfying the SUSY invariance. Contrary to
the Abelian gauge group, it is not essential to introduce the new operator in
order to check the exact SUSY invariance of the Lagrangian density. However, in
order to introduce the (0,2) chiral superfields, we need the $\hat{U}$
operator, because we can not define the (0,2) chirality conditions of the (0,2)
chiral superfields without introducing the new operator by using $\hat{U}$ and
the enlarged operator \hat{U}^{a} was obtained from the conditions that yield
the (0,2) supersymmetric invariance of the Lagrangian density of the (0,2) U(N)
gauged linear sigma model in superfield formalism. We found that the
consistency conditions for the Abelian gauge group which assure the (0,2)
supersymmetric invariance of Lagrangian density agree with (0,2) chirality
conditions for superpotential. The supermanifold \mathcal{M}^{m|n} becomes the
super weighted complex projective space WCP^{m-1|n} in U(1) case, which is
considered as an example of Calabi-Yau supermanifold.
