Abstract: We construct a new Fukaya category of Landau-Ginzburg model defined by weighted homogeneous polynomials and their symmetry group. From wrapped Fukaya category and monodromy information on the Milnor fiber we define a new $A_\infty$-category and especailly its equivariant version. As an application, we prove Berglund-H\"ubsch homological mirror symmetry for curve singularity.