Given a dominating set S ⊆ V(G) for a graph G, each vertex of the graph is either in S or is adjacent to at least one vertex in S. The set S is a secure dominating set of G if, for each vertex u ∈ V(G)\S, there exists a vertex w ∈ S adjacent to u such that (S\{w})∪{u} is also a dominating set of G. The minimum cardinality of a secure dominating set in G determines the secure domination number of G. A prior investigation has established an upper bound for the secure domination number of Pp × Pq. Also, the exact values of the secure domination numbers of P2 × Pn and P3 × Pn have been reported in the literature. We present an improved upper bound for the secure domination number of Pn × Pn, when n ≥ 4 and n ≡ s (mod 3), where s ∈ {1, 2}. Using the improved upper bound, we provide an upper bound for the secure domination number of pyramid networks.