The　connectivity　of　a　graph　is　a　classic　measure　for　fault　tolerance　of　the　network.　Restricted　connectivity　measure　is　a　crucial　subject　for　a　multiprocessor　system＇s　ability　to　tolerate　fault　processors,　and　improves　the　connectivity　measurement　accuracy.　Furthermore,　if　a　network　possesses　a　restricted　connectivity　property,　it　is　more　reliable　with　a　lower　vertex　failure　rate　compared　with　other　networks.　The　-dimensional　enhanced　hypercube,　denoted　by　,　a　variant　of　hypercube,　which　is　a　well-known　interconnection　network.　In　this　paper,　we　analyze　the　fault　tolerant　properties　for　-enhanced　hypercube,　and　establish　the　-restricted　connectivity　of　and　-restricted　connectivity　of　-enhanced　hypercube　.　Furthermore,　we　propose　the　tight　upper　bound　of　-restricted　connectivity　of　.　Moreover,　we　show　many　figures　to　better　illustrate　the　process　of　the　proofs.