Most recent schema matching systems combine multiple components, each of which employs a particular matching technique with several knobs. The multi-component nature has brought tuning problems for domain users. In this paper, we present GATuner, an approach to automatically tune schema matching systems using genetic algorithms. We match a given schema S against generated scenarios, for which the ground truth matches are known, and find a configuration that effectively improves the performance of matching S against real schemas. To search the huge space of configuration candidates efficiently, we adopt genetic algorithms during the tuning process. Experiments over four real-world domains with two main matching systems demonstrate that our approach provides more qualified matches over different domains.