The main purpose of this study is to develop indices of the core competence for undergraduates in Taiwan and to explore the status quo of Taiwanese undergraduates¡¦ basic competence. Questionnaire survey was conducted in this research and based on The Indices of Undergraduates¡¦ Core Competence Scale. The scales in the study consist of 6 subscales of Basic & Professional Abilities, Creativity & Problem-solving Capability, Interpersonal Communication Skill, Moral & Civic Literacy, International Visions and Self-directed Learning to explore the important competence and literacy and the possessed competence and literacy. There were totally 642 subjects of three groups, including 113 superintendents, 116 professors, and 413 undergraduates. Data were analyzed through descriptive statistics, one-way ANOVA, one-way MANOVA, and Rasch analysis. The results indicated: (a) each subscale of each scale had reasonable Cronbach £\ ranging from .77 to .97 and the overall model fit statistics indicated that model fitted the observed data; (b) all subjects considered that undergraduates¡¦ competence was above average on the dimensions of the important competence and the possessed competence, except that the professor group considered that undergraduates¡¦ competence did not achieve average level on Creativity & Problem-solving Capability, International Visions, and Self-directed Learning of Possessed Competence and Literacy; (c) there were significant differences in different classes of superintendents, different genders and different grades of the undergraduates on Important Competence and Literacy for Undergraduates; (d) the items of important and not possessed considered by superintendents and professors were ¡§problem-solving skills,¡¨ ¡§wide visions,¡¨ ¡§foreign language skills,¡¨ ¡§setting learning goals and strategies,¡¨ ¡§evaluating learning achievements,¡¨ ¡§critical thinking skills,¡¨ ¡§managing learning environment,¡¨ and ¡§keen perception,¡¨ and the items of important and not possessed considered by undergraduates were ¡§foreign language skills,¡¨ ¡§making use of learning resource,¡¨ ¡§professional erudition,¡¨ ¡§capacity of logic analysis,¡¨ ¡§reflecting the effects of learning.¡¨ Suggestions were proposed as reference for college education policies, general courses, and future studies.