STEAM education cultivated implementation, invention, and innovation, and advocated the educational principles of “cross-domain, implementation, application, problem-solving, and five-sense learning.” In this study, teachers’ acceptance and satisfaction with STEAM teaching were explored using the fuzzy analytical hierarchy process by determining the weight of criteria that teachers valued. 80 teachers participated in the questionnaire survey. The collected responses were analyzed using the multi-criteria decision-making and problem-solving method to make reasonable solutions to complex problems of STEAM teaching. The result showed that teachers’ acceptance and satisfaction were most important in implementing STEAM education. At the same time, teachers need to improve their professionalism and capabilities in STEAM courses to improve students’ design and innovation literacy. In addition, learning needs to be integrated into the curriculum and sufficient time needs to be provided for smooth promotion. When teachers were satisfied with the integrated STEAM education, the students’ improvement in design innovation literacy and learning results were observed in this study. Experience and background knowledge affect effectiveness in teaching and learning. Also, “ease of learning and acceptance” and “ease of integration into teaching” were found to be important criteria for teachers to improve professionalism, increase the investment of their resources in teaching, and overcome the difficulties of learning. To enhance the professionalism of teachers, appropriate knowledge and curriculum reform is demanded through the interdisciplinary education of STEAM courses.