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A Recently, Ghorbani et. al. introduced the eccentric versions of first and second Zagreb indices called third and fourth Zagreb indices defined asM3 (G) = Σuv∊E(G) (ε (u) + ε (ν)) and M4 (G) = Σν∊V(G)ε (ν)2, respectively, where ε (ν)is the eccentricity of the vertex ν. In this paper, we compute the closed formula for third Zagreb index of Polycyclic Aromatic Hydrocarbons (PAHk).