Most　of　the　recent　results　on　the　leader-following　rendezvous　problem　focus　only　on　the　deterministic　multi-agent　systems　without　external　disturbances　and　parameter　uncertainties.　In　this　paper,　we　will　present　a　novel　distributed　internal　model　approach　to　study　the　leader-following　rendezvous　problem　for　double-integrator　multi-agent　systems　subject　to　both　external　disturbances　and　parameter　uncertainties.　We　first　give　some　suitable　distributed　internal　model　to　convert　the　rendezvous　problem　into　the　stabilization　problem　with　connectivity　preserving　for　its　augmented　system.　Then　we　stabilize　the　corresponding　augmented　system　via　distributed　state　feedback　control　by　defining　a　new　potential　function　and　performing　the　backstepping　control　technique.　Comparing　with　some　recent　results,　our　design　can　handle　a　large　class　of　reference　signals,　external　disturbances,　and　plant　uncertainties.