Memetic algorithms (MAs) with multiple Local Search Strategies (LSSs) for the mixed H-infinity/H-2 robust control design is proposed and investigated in this paper. Multiple LSSs are introduced into a given evolutionary computation leading to a new memetic algorithm. The correcting memes, directed memes, and stochastic memes are used to form the meme pool for iterative search, by which the multiple LSSs can be combined with Multi-Objective Evolutionary Algorithms (MOEAs) together. The new algorithm is applied in Multi-objective Robust Control Design (MRCD), which is capable of both moving toward and along the Pareto can yield a better performance for these two norms. Finally, the result of the proposed memetic algorithm is compared with the numerical solution of the convex approximations in terms of the Linear Matrix Inequalities (LMIs).