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Let G be a simple connected graph. The second Gourava index of graph G is defined as G O 2 G = ∑ θ ϑ ∈ E G d θ + d ϑ d θ d ϑ where d θ denotes the degree of vertex θ. If removal of a vertex of G forms a tree, then G is called an apex tree. Let L ⊂ V G with ∣ L ∣ = q. If removal of L from V G forms a tree and any other subset of V G whose cardinality is less than ∣ L ∣ does not form a tree, then G is known as q -apex tree. In this paper, we have calculated upper bound for 2 nd Gourava index with respect to q -apex trees. [ABSTRACT FROM AUTHOR]