The main purposes of this study are to explore the theoretical foundation about elememtary school principal’s leadership competence;and to analyze the critical and framework of indicators measuring principal’s leadership competence. Literature review and questionnaires survery were conducted in this study. gathered from stakeholder’s opinion help to constitute data base of this research, The stakeholders include 9 scholars,6 administrational personnel,9 elememtary pr incipa ls, a nd 8 school teachers.The tools applied is“Delphi investigation questionnaires about elememtary school principal’s leadership competence”and “Analytic hierarchy process vestigation questionnaires about elememtary school principal’s leadership competence”. The triangula r fuzzy number and Hiera rchy analytic process of evaluation indicators are base on Micrrosoft Windows 2003 Sever+IIChinese Edition APSScript language author’s own inventive Web online discriminative calculation system with EXCEL 2000。 All of the indicators mentioned are tools to evaluate elememtary school principal’ s leadership competence.