In the RNA world hypothesis, RNA(-like) self-replicators have been suggested as the central player of prebiotic evolution. However, there is a serious problem in the evolution of complexity in replicator systems, i.e., the problem of parasites: The parasite exploits altruistic replicators and thus hinders the evolution of cooperatively coupled replicator system. To investigate a possibility of the evolution of complexity in an RNA replicator system, we here simulate the evolutionary dynamics of a hypothetical RNA replicator by using RNA folding as a genotype-phenotype map. The results show a remarkable stability of the replicator system despite the evolution of parasitic replicators in both ecological and evolutionary time scales. Moreover, we illustrate the role of the parasitic replicators as a possible substrate for the evolution of complexity.