A minimum vertex-cut set of a connected fuzzy graph T = (V, E, κ, λ), abbreviated MVC, is a vertex-cut set with minimum cardinality. Let W be an MVC set of T. The strength of W is defined as the S(W) = max{min{λ(p, q)|q ∈ V\W}|p ∈ W}. The maximum value of the strength of all MVC sets of T = (V, E, κ, λ) is called high strength connectivity of graph T and represented by HS(T). In this article, the high strength connectivity of the vertex-cut set in famous fuzzy graphs was determined. Also, an algorithm was introduced to calculate high strength connectivity in these graphs by using Sage software. Examples of the high strength connectivity applications in economic and power plant were given.