Teaching speaking for English-as-a-Foreign-Language (EFL) students in an English-for-Specific-Purposes (ESP) classroom is a demanding process. Despite the efforts of the Vietnamese government and educators, many Vietnamese EFL students perceive speaking as one of the most challenging language skills, and their speaking abilities in real-life situations are insufficient to fulfill society's increasing demands. As a result, it is the role of language teachers to identify students' difficulties in speaking English and help them enhance their language speaking skills. This paper aims to explore the English speaking problems faced by ESP Vietnamese learners at the University of Foreign Language Studies, University of Danang (UFLS-UD), Vietnam . A questionnaire was employed to collect data from first-year undergraduate students in the ESP Department at UFLS-UD. Besides, the study also proposed a scaffolding model named "Diagnosing, Modeling and Sharing, Guiding, Applying" (DMGA) as a practical suggestion for EFL teachers for speaking training. It is hoped that the findings of the study will benefit both Vietnamese education policy makers, teachers as well as students in terms of teaching and learning speaking skills in ESP settings within an EFL context.