Decentralized autonomous organizations (DAOs) have become an indispensable part of digital infrastructure in recent years. The unique organizational characteristics and functional structure empower them to become an effective tool for solving corporate governance issues, including contract risks, principal-agent dilemmas, etc. However, DAOs themselves also face a variety of governance issues. On one hand, as a new economic organization model, the existing corporate governance theories and methods are no longer fully applicable to DAOs. On the other hand, unpredictable logic vulnerabilities and code loopholes in the governance mechanism might cause devastating damage to DAOs. The parallel intelligence theory based on the ACP method (i.e., artificial systems, computational experiments, and parallel execution) is an elegant research paradigm and a practical approach tailored to solving these challenges. As such, we propose a novel parallel governance framework for DAOs based on the parallel intelligence theory and further discuss its technical methodology and implementation model. Furthermore, we construct a parallel governance system for GnosisDAO and conduct computational experiments to validate the effectiveness of its governance mechanism. The experimental results not only confirm the defects of the GnosisDAO governance mechanism but also illustrate parallel governance as a useful research direction to solve existing governance problems of DAOs.