In the paper [3]，the more general concept of fuzzy ideals was introduced，and the study of fuzzy algebraic Structure has been developed. In this paper，we make a study of another topic in the fuzzy Structure theory. The notion of the fuzzy Subfields is suggested. The Structure problems of the fuzzy subfields on the finite extension fields are discussed in detail Several representatiue theorems which are analogous to those in [2] are obtained. Later，the notion of induced fuzzy subfields is introduced，we study the properties of the induced fuzzy subfields on the Simple algebraic extonsion fields