It is shown that the algebra associated with the local Kappa-supersymmetry in the Green-Schwarz superstring theory in d = 2 dimensions closes off shell. We quantize the theory in a Lorentz covariant fashion by using the generalized hamiltonian method of Batalin, Fradkin and Vilkovisky, and derive a quantum mechanically consistent, gauge-fixed theory, which can be interpreted as a Kappa-supersymmetric extension of conformal topoligical gravity.