Our purpose is to give an overview of weak topologies in a fuzzy locally convex space. Firstly, we introduce locally convex spaces in fuzzy context. Furthermore fuzzy version of a semi - norm is obtained. Finally, we introduce a weak topology on a fuzzy locally convex space and the weak star topology on its dual as a generalization of usual weak topology. A special attention is also given to some properties of X- topology on X*, called fuzzy weak star topology.