As an essential language component, grammar plays a crucial role in communication. However, with the need to master various L2 forms within several years and an L1 that has a very different grammatical system from English, many tertiary EFL students find grammar learning challenging. To solve this issue, peer teaching/tutoring can be a very effective way to assist students in improving their grammar. While isolated grammar teaching has its downsides, it is superior in clarifying complex concepts and promoting accuracy. It may help increase students’ grammar competence when combined with other methods as an eclectic approach used in a communicative language program. As grammar tutors play a crucial role in helping their peers, this study examines the challenges they perceive in peer tutoring at the tertiary EFL education level and their strategies for overcoming difficulties. Using interviews to collect data from ten EFL grammar tutors, this qualitative study revealed some issues the tutors faced. Besides identifying problems such as motivating students, preparing the materials, and dealing with less/more proficient students, this research demonstrated that peer teaching might lead to ‘cognitive dependence’ among the lower-level learners. To deal with the various issues, the peer tutors applied practical strategies they had developed mainly from intuition and experience.