Abstract: When Humans enter the 21st century, the new technologies, new industries and their new forms, and new modes have been emerging, which bring the new chance and challenges for the English education. All these have posed the new requirement for cultivation of core competence of these students. Under such "four New" background, the core competence of normal university students majoring in English includes competence of professional ethics, knowledge, ability, learning and development, group and fighting spirit. To cultivate such competence, some strategies can be taken, such as construction of multiple teaching mode, promotion of practice, improvement of automatic leaning and innovation, and strengthening the education of cultural awareness.