Although a good number of studies have been conducted on the problems EFL learners face to develop oral English communication skills, only a few studies tackled the problems EFL teachers face when teaching oral English communication skills at the tertiary level globally and in the Bangladeshi EFL context. Thus, the objectives of this study are to explore the problems faced by EFL teachers and the relationship between teachers' demographic factors and the problems of teaching oral English communication skills (OECSs) at the tertiary level in Bangladesh. To obtain these objectives, the researchers employed an explanatory sequential mixed-method research design by distributing an adapted survey questionnaire and conducting a semi-structured interview. Data were collected from 46 EFL teachers who were teaching at the department of English at 15 different public and private universities in Bangladesh. The synthesized results from quantitative and qualitative data show that the most frequent problems that EFL teachers face are the use of mother tongue, inappropriate teaching method, learners' passiveness, and lack of motivation, lack of oral practice environment, lack of supporting tools, lack of authentic materials and large class size. Besides, there is no statistically significant relationship between teachers' demographic factors and the problems the teachers face while teaching oral skills at the tertiary level in Bangladesh. In light of the results, this paper recommends that empirical studies should be conducted to provide teachers with methods that would integrate features of the smartphone, such as WhatsApp, call recorder, voice recorder etc. for teaching oral English communication skills.