Due　to　the　development　of　multi-energy　conversion　technologies　and　the　higher　public　awareness　of　the　sustainability,　the　energy　system　has　begun　a　transition　toward　the　energy　hub　(EH)　based　integrated　energy　system　(IES).　This　paper　proposes　a　distributed　robust　synergistic　scheduling　method　for　multi-EH-based　IES　coupled　with　electricity,　natural　gas,　heating　and　cooling,　to　minimize　the　operating　cost　of　the　IES　while　considering　the　uncertainties　of　renewable　generations　(RGs)　and　multi-energy　load　demands.　The　nonconvexity　of　energy　network　constraints,　uncertainties　in　multiple　EHs　as　well　as　limitation　of　information　exchange　lead　to　significant　challenges　for　IES　scheduling.　To　deal　these　issues,　the　original　robust　scheduling　model　of　IES　is　first　reformulated　as　a　mixed　integer　second-order　cone　programming　(MISOCP)　by　convex　relaxation　method.　Furthermore,　to　improve　the　economy　and　flexibility　of　robust　scheduling　solution,　a　light　robust　model　is　developed　to　address　the　multiple　uncertainties　from　EHs.　Finally,　a　consensus-based　alternating　direction　method　of　multipliers　(ADMM)　approach　is　developed　to　tackle　the　robust　scheduling　model　in　MISOCP　form,　where　EH　operators　parallelly　solve　their　respective　EH　subproblems　with　limited　information　exchange,　and　subsequently　the　EH　subproblem　in　MISOCP　form　is　solved　by　a　nonconvex　ADMM　(NC-ADMM)　approach　to　guarantee　the　convergence　of　the　consensus-based　ADMM.　Simulation　results　in　a　three-EH　IES　are　presented　to　illustrate　the　effectiveness　of　proposed　method　for　optimal　synergy　of　multiple　EHs　with　uncertainties.