For an undirected graph G, a set \(S \subseteq V(G)\) is a secure dominating set (SDS) of G if each vertex \(v \in V (G) -S\) has a neighbor \(u \in S\) such that the set \((S - \{u\}) \cup \{v\}\) is a dominating set of G. Secure domination number of a graph G denoted by \(\gamma _s(G)\) is the minimum cardinality of a SDS of G. Given a graph G, determining \(\gamma _s(G)\) is termed as secure domination problem (SDOM). SDOM is NP-hard and hence not polynomial time solvable. Since SDOM problem has applications in facility location, communication networks and other social networks, proposing an efficient polynomial-time algorithm can help tackle the limitations faced in applications. To the best of our knowledge, unlike domination problem, there are no known metaheuristic algorithms for SDOM problem. In order to counter this, a genetic algorithm-based solution to solve SDOM problem is proposed in this paper. The proposed algorithm uses a heuristic to generate a population of feasible solutions and generate a better feasible solution by passing it through various steps of genetic algorithm. Proposed genetic algorithm for SDOM problem has been tested on graphs for which optimal values are known, random graphs and HB graphs. Since there exists no metaheuristic algorithm for solving the SDOM problem, our results set a benchmark for future research on the SDOM problem.