Let  be a fuzzy Graph. Let  denote respectively the domination number, the point set domination number and the connected point set domination number of a fuzzy graph. A dominating set D of a fuzzy graph is said to be a point set dominating set of a fuzzy graph if for every  there exists a node  such that  is connected fuzzy graph. The minimum cardinality taken over all minimal point set dominating set is called the point set domination number of a fuzzy graph G and it is denoted by . A point set dominating set D of any fuzzy graph G is a connected point set dominating set if the fuzzy subgraph induced by D is connected. The minimum cardinality taken over all point set dominating set of a fuzzy graph G is said to be connected point set domination of a fuzzy graph G. It is denoted by . In this paper we concentrate on connected point set domination number of fuzzy graph and obtain some interesting results for new parameter of fuzzy graphs.