The　quantum　swap　gate　is　one　of　the　most　useful　gates　for　quantum　computation.　Two-qubit　entanglement　and　a　controlled-NOT　quantum　gate　in　a　neutral　Rydberg　atom　system　have　been　achieved　in　recent　experiments.　It　is　therefore　very　interesting　to　propose　a　scheme　here　for　swapping　a　quantum　state　between　two　trapped　neutral　atoms　via　the　Rydberg　blockade　mechanism.　The　atoms　interact　with　a　sequence　of　laser　pulses　without　individual　addressing.　The　errors　of　the　swap　gate　due　to　imprecision　of　pulse　length,　finite　Rydberg　interaction,　and　atomic　spontaneous　emission　are　discussed.