Let　r≥2　and　(Xi,G)　(i=1,⋯,r)　be　topological　dynamical　systems　with　an　infinite　countable　discrete　amenable　phase　group　G.　Suppose　that　πi:(Xi,G)→(Xi+1,G)　are　factor　maps,　a={a1,⋯,ar−1}∈Rr−1　is　a　vector　with　0≤ai≤1　and　(w1,⋯,wr)∈Rr　is　a　probability　vector　associated　with　a.　In　this　paper,　given　f∈C(X1),　we　introduce　the　weighted　topological　pressure　Pa(f,G).　Moreover,　by　using　measure-theoretical　theory,　we　establish　a　variational　principle:　Pa(f,G)=supμ∈MG(X1)⁡(∑i=1rwihμ(Xi,G)+w1∫X1fdμ),　where　h{⋅}(⋅,G)　is　the　Kolmogorov-Sinai　entropy　of　the　systems　acted　by　the　amenable　group　G　and　μi=πi−1∘⋯∘π1μ　is　the　induced　G-invariant　measure　on　Xi.　©　2024　Elsevier　Inc.