In Asia, in order to keep up with internationalization, the English-Medium Instruction (EMI) course has become a phenomenon in higher education. In turn, EMI literature has increasingly focused on the role of instructor's pedagogy in reducing students' negative response to EMI courses. Additionally, we further explore, from the students' perspective, whether students can reduce their anxiety about learning in English by adopting varied learning strategies while reducing their avoidance of EMI courses. A questionnaire survey was conducted in spring 2018; 208 postgraduate students from 15 different EMI courses in the School of Business Administration of a Taiwanese University participated in this study. We used partial least-squares structural equation modelling (PLS-SEM) to explore the relationship between learning strategies, English anxiety, and EMI avoidance, while regarding English proficiency as a controlled variable. The results indicate that English anxiety has a positive relationship to EMI avoidance; critical thinking has a negative relation to English anxiety; effort regulation has a negative relation to EMI avoidance, and English anxiety mediates the relationship between critical thinking and EMI avoidance. General principles are drawn from these findings and are discussed as they apply to the teaching of EMI classes.