In this paper we introduce the concept of Para-Lindelof spaces in L-topological spaces by means of locally countable families of L-fuzzy sets. Further some characterizations of fuzzy para-Lindelofness and flintily para-Lindelofness in the weakly induced L-topological spaces are also obtained. More over the behavior of fuzzy para-Lindelof spaces under various types of maps such as fuzzy closed maps, fuzzy perfect maps are also investigated.