The first and second Zagreb indices is defined as ( )2 v V (G) d v Î Σ and ( ) ( ) uv E(G) d u d v Î Σ , respectively, where d(v) is the degree of the vertex v. Recently, Ghorbani et. al. proposed the eccentric version of Zagreb index called fourth Zagreb index as ( ) ( ) 2 v V G e v Î Σ , where e (v) is the eccentricity of the vertex v. In this paper, we compute the exact formulae for the Polycyclic aromatic hydrocarbon (PAHk).