  We develop a $G$-equivariant Lagrangian Floer theory and obtain a curved
$A_\infty$ algebra, and in particular a $G$-equivariant disc potential. We
construct a Morse model, which counts pearly trees in the Borel construction
$L_G$. When applied to a smooth moment map fiber of a semi-Fano toric manifold,
our construction recovers the $T$-equivariant toric Landau-Ginzburg mirror of
Givental. We also study the $\bS^1$-equivariant Floer theory of a typical
singular SYZ fiber (i.e. a pinched torus) and compute its $\bS^1$-equivariant
disc potential via the gluing technique developed in \cite{CHL18,HKL}.
