Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. The BFV-BRST quantization applies to formulate the theory in the most general class of gauges. A local effective action constructed in the configuration space contains two super-Liouville actions; one is a noncovariant but local functional written only in terms of two-dimensional supergravity fields, and the other contains the super-Liouville fields canceling the super-Weyl anomaly. Auxiliary fields for the Liouville and the gravity supermultiplets are introduced to make the BRST algebra close off-shell. Inclusion of them turns out to be essentially important especially in the super-light-cone gauge fixing, where the supercurvature equations (${\mathrm{\ensuremath{\partial}}}_{\mathrm{\ensuremath{-}}}^{3}$${\mathit{g}}_{++}$=${\mathrm{\ensuremath{\partial}}}_{\mathrm{\ensuremath{-}}}^{2}$${\mathrm{\ensuremath{\chi}}}_{++}$=0) are obtained as a result of BRST invariance of the theory. Our approach reveals the origin of the OSp(1,2) current algebra symmetry in a transparent manner. \textcopyright{} 1996 The American Physical Society.