The min-max theory was proposed by Almgren in the 1960s to find minimal hypersurfaces in compact manifolds. Subsequently, Pitts and Schoen-Simon advanced this theory in the 1980s for compact manifolds without boundary. In this talk, we consider a closed Riemannian manifold M with a compact Lie group G acting by isometries. Then we construct a G-invariant minimal hypersurfaces by the equivariant min-max theory under the setting of Almgren-Pitts. As applications, we show the growth of the equivariant volume spectrum and some further results on the index and topology of equivariant min-max hypersurfaces.