The current study aimed at diagnosing the language needs of Iranian undergraduate students of computer engineering in order to find out whether there is any significant difference in perceptions between the students and their ESAP (English for Specific Academic Purpose) teachers, concerning their Reading skill needs. To conduct the intended research study, both qualitative and quantitative approaches were taken. The quantitative approach included the use of self-assessment, and two questionnaires, and the qualitative approach included participant observation. The questionnaires were adapted from Atai and Shoja (2009), and were distributed among 500 undergraduate students of computer engineering and 30 ESAP teachers who were chosen randomly through cluster sampling method from thirteen universities. Mann-Whitney U-test results showed that there was a significant difference between perceptions of the students and their teachers about their Reading skill needs and "Reading" was mentioned as one of the most difficult skills for the students. Moreover, it was found that the majority of students suffered from low level of General English Language Proficiency, and also "low motivation" and the "character" of teachers were found to be important factors affecting students' learning.