With the background of internalization and globalization of higher education, whether graduates are capable of international academic cooperation and communication or not is determined by their academic communicative competence. Yanan University was listed the high-level university construction program of Shaanxi in 2011. At present, graduates number takes one tenth of the undergraduates (according to the official website in April, there are 1462 graduates and 15683 undergraduates in Yanan University). Therefore, Yanan University is a representative among western provincial universities. This thesis explores the present situation of non-English major graduates' academic English communicative competence in western provincial universities through interview and questionnaire, and puts forward to several related countermeasures in improving their academic English communicative competence.