Summary: Let \(G=(V,E)\) be a graph. Let \(D\) be a minimum secure dominating set of \(G\). If \(V-D\) contains a secure total dominating set \(D'\) of \(G\) then \(D'\) is called an inverse secure dominating set with respect to \(D\). The smallest cardinality of inverse secure dominating set of \(G\) is the secure domination number \(\gamma_s^{-1}(G)\) of \(G\). In this paper, we obtain some graphs for which \(\gamma_s(G)= \gamma_s^{-1}(G)\) and establish some results on this respect. Also we obtain some graphs for which \(\gamma_s(G)=\gamma_s^{-1}(G)=p/2\), where \(p\) is the number of vertices of \(G\).