Focusing on whether fuzzy system can approximate any given function, the sufficient and necessary theory of one type of fuzzy systems as universal approximators was investigated. Mamdani fuzzy systems with product inference engine (PIE) and mean of maximum (MOM) defuzzificator can be classified two cases according to rule consequent: simple point rule consequent and fuzzy set rule consequent. Based on Weierstrass's first theorem and properties of membership functions, sufficient and necessary condition is proved respectively. A simulation example is given to show the effectiveness of the proposed method.