  We investigate space-time supersymmetry in the WZW-like open superstring
field theory, whose complete action was recently constructed. Starting from a
natural space-time supersymmetry transformation at the linearized level, we
construct a nonlinear transformation so as to keep the complete action
invariant. Then we show that the transformation satisfies the supersymmetry
algebra up to an extra transformation, unphysical on the asymptotic string
fields. This guarantees that the constructed transformation in fact acts as
space-time supersymmetry on the physical S-matrix.
