In this paper,the geometric properties of fuzzy complex plane are studied by the concept of the com-plex fuzzy point and complex fuzzy line proposed in the fuzzy complex plane.The fuzzy complex distance is de-fined and proved to be a(weak)fuzzy complex metric between two fuzzy complex points.The fundamental prop-erties of the complex fuzzy line are discussed.Meanwhile,the fuzzy complex line segments,parallel,and intersec-ting fuzzy complex lines are studied and some examples are given to illuminate the results obtained in this paper.