After ChatGPT sparked widespread global interest in Generative AI (GenAI), people have shown a keen interest in this technology. Various fields are actively employing GenAI. Scholars’ opinions regarding GenAI are diverse; however, it undoubtedly signifies a significant technological leap. Nevertheless, there has been extensive discussion within the academic community about the potential benefits and harms of GenAI in the future. Yet, empirical research on this subject is relatively scarce, especially concerning the student population, which extensively utilizes this technology. And the variations in national cultures might contribute to differing attitudes and perspectives among students toward GenAI. This research investigates the intention of university students to use GenAI by employing an integrated model combining the Technology-Organization-Environment (TOE) framework and the Technology Acceptance Model (TAM). External variables encompassed technological dimensions of innovation, trust, and risk; organizational dimensions of GenAI knowledge competency and cost; and environmental dimensions of policies and regulations and societal influence. Internal factors included perceived usefulness and perceived ease of use from the TAM. The ultimate dependent variable examined was the intention to use GenAI. Survey data were collected from university students in two countries, China and South Korea, comprising 400 and 344 samples, respectively. A Structural Equation Modeling (SEM) analysis was conducted to explore the relationships between variables. By comparing the differences between the two countries, this study found and determined the moderating role of cultural influences. This research will provide far-reaching insights and guidance for the students’ future development, education changes, GenAI product development, AI-related legal making, and cross-cultural research.