  In this paper, we define the set of singular grid diagrams $\mathcal{SG}$
which provides a unified description for singular links, singular Legendrian
links, singular transverse links, and singular braids. We also classify the
complete set of all equivalence relations on $\mathcal{SG}$ which induce the
bijection onto each singular object. This is an extension of the known result
of Ng-Thurston for non-singular links and braids.
