Abstract Let G be a simple graph. We say that a hypergraph H is a Berge-G if there is a bijection ϕ : E ( G ) → E ( H ) such that e ⊂ ϕ ( e ) for all e ∈ E ( G ) . For any r-uniform hypergraph H and a real number p ≥ 1 , the p-spectral radius λ ( p ) ( H ) of H is defined as λ ( p ) ( H ) : = max ‖ x ‖ p = 1 ⁡ r ∑ { i 1 , i 2 , … , i r } ∈ E ( H ) x i 1 x i 2 ⋯ x i r . In this paper we study the p-spectral radius of Berge-G ( G ∈ C n + ) hypergraphs and determine the 3-uniform hypergraphs with maximum p-spectral radius for p ≥ 1 among all Berge-G ( G ∈ C n + ) hypergraphs, where C n + is the set of graphs of order n obtained from C n by adding an edge.