This study proposes a lesson design framework to design a science and engineering integrated lesson in a meaningful and easy way based on engineering design, which is the core feature of STEM education. The science and engineering integrated lesson design framework is developed based on the analysis of domestic and foreign theoretical and practical research papers and expert discussion on science and engineering integrated education as well as the feedbacks from science teachers. The science and engineering integrated lesson design framework uses engineering design as the main pedagogical method. The framework includes the core elements of the engineering integrated lesson suggested in previous studies and the achievement level of each grade group suggested in NGSS and provides a way for teachers to easily introduce engineering design into science classes. In addition, the framework developed in this study complements the shortcomings of the complicated Korean STEAM education framework. It can also provide specific guidance to in-service teachers as well as pre-service teachers to easily understand and apply engineering design and problem solving processes to science and engineering integrated lessons.