The National Museum of Natural Science (NMNS) was established in 1986. By 1999, the NMNS exceeded the 3 million visitors mark, surpassing the National Palace Museum to become Taiwan’s largest museum, and established itself as one of the top five museums in the world. From 1999 to 2008, the NMNS received more than 3 million visitors, attaining the status of being the single most important leisure destination for the people of Taiwan. Like other Taiwanese museums, NMNS faces strong competition from other tourist and leisure attractions. How to attract more visitors will continue to be a challenge for years to come, and consequently the long-term satisfaction of visitors has become a key issue. The problem of satisfying visitors is dynamic and complicated involving the interaction of many factors such as government policies, museum service quality, visitor expectations, and social environments. This study utilized system dynamics approach to investigate the system structure of factors affecting the long-term satisfaction of NMNS visitors. The results showed that long-term satisfaction could be affected by the interaction of factors such as the quality of service, the availability of facilities, and accumulated number of visitors. Finally, this study simulated the implementation of a number of relevant policies; discussing the implications and results.