In　this　letter,　we　study　the　performance　of　protograph-based　low-density　parity-check　(LDPC)　codes　for　two-user　Gaussian　multiple　access　channel　(GMAC).　Considering　the　characteristic　of　a　joint　protograph　of　two　users,　we　first　derive　a　joint　protograph-based　extrinsic　information　transfer　(JP-EXIT)　chart　to　analyze　the　iterative　user　decoding　behavior　of　two-user　GMAC.　Guided　by　the　JP-EXIT,　we　further　propose　a　new　design　scheme　and　construct　protograph　base　matrices　of　different　code　rates　for　two　users,　respectively.　Both　theoretical　analyses　and　simulation　results　show　that　the　proposed　protograph-based　LDPC　codes　of　low　decoding　threshold　outperform　the　conventional　irregular　LDPC　codes　for　both　equal-power　and　unequal-power　GMAC　with　different　code　rates.