Abstract: As computer networks continue to grow, it becomes increasingly more important to automate the process of evaluating their vulnerability towards attacks. Despite the best efforts of software architects and developers, network hosts inevitably contain a number of vulnerabilities. Attack graphs are models that offer significant capabilities to analyze security in network systems. An attack graph allows the representation of vulnerabilities. We model compositions of vulnerabilities through attack graphs. This study proposes a Memetic based method to explore the graph attack. Each attack path is considered as an independent attack scenario from the source of attack to the target. Many such paths form the individuals in the evolutionary Memetic solution. The population-based strategy of a Memetic provides a natural way of exploring a large number of possible attack paths to find the paths that are most important. Simulated annealing is used as local optimizer in proposed Memetic algorithm. A comparison was made between presented algorithm and Memetic Particle Swarm Optimization algorithm. Experimental results proved that Memetic based algorithm for minimization analysis of network attack graph is accurate and has better performance.