In order to solve reliability-redundancy allocation problems more effectively, a new hybrid algorithm named CDEPSO is proposed in this work, which combines particle swarm optimization (PSO) with differential evolution (DE) and a new chaotic local search. In the CDEPSO algorithm, DE provides its best solution to PSO if the best solution obtained by DE is better than that by PSO, while the best solution in the PSO is performed by chaotic local search. To investigate the performance of CDEPSO, four typical reliability-redundancy allocation problems were solved and the results indicate that the convergence speed and robustness of CDEPSO is better than those of PSO and CPSO (a hybrid algorithm which only combines PSO with chaotic local search). And, compared with the other six improved meta-heuristics, CDEPSO also exhibits more robust performance. In addition, a new performance was proposed to more fairly compare CDEPSO with the same six improved meta-heuristics, and CDEPSO algorithm is the best in solving these problems.