  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 2D supergravity fields, and the other
contains the super-Liouville fields canceling the super-Weyl anomaly. Auxiliary
fields for the Liouville and the gravity super-multiplets are introduced to
make the BRST algebra close off-shell. Inclusion of them turns out to be
essentially important especially in the super-lightcone gauge-fixing, where the
super-curvature equations ($\dl^3_-g_{++} =\dl^2_-\chi_{++}=0$) are obtained as
a result of BRST invariance of the theory. Our approach reveals the origin of
the graded-SL(2,R) current algebra symmetry in a transparent manner.
