  In this paper, for any compact Lie group $G$, we show that the space of
$G$-invariant Riemannian metrics with positive scalar curvature (PSC) on any
closed three-manifold is either empty or contractible. In particular, we prove
the generalized Smale conjecture for spherical three-orbifolds. Moreover, for
connected $G$, we make a classification of all PSC $G$-invariant
three-manifolds.
