Megaprojects are characterized by significant environmental uncertainty and technical complexity, which bring great challenges to engineering construction. Cross-organizational collaborative innovation is an important way to solve these problems. As the main body that understands the difficulties of the construction site and uses innovative products, the participation of megaproject participants is not only conducive to increasing innovation efficiency but also conducive to the application and promotion of innovative achievements. The collaborative innovation behavior of the participants in megaprojects under the reward and punishment incentive mechanism was studied. A game model between different participants was built by combining evolutionary game theory with prospect theory. Then, the dynamic evolution process of the collaborative innovation strategy of participants was analyzed, and the main factors affecting the evolutionary stability strategy of collaborative innovation through numerical simulation were examined. The research results indicate that reward and punishment incentives of collaborative innovation can encourage participants to choose the evolutionary stability strategy of participating in collaborative innovation from both objective and subjective aspects. Factors, such as the cost of participating, the synergy coefficient, the proportion of collaborative revenue distribution, and risk preference, can influence participants’ willingness to engage in collaborative innovation to different degrees.