Weak　fault　detection　is　a　complex　and　challenging　task　when　two　or　more　faults　(i.e.　a　compound　fault)　with　discordant　severity　occur　in　different　parts　of　a　gearbox.　The　weak　fault　features　are　prone　to　be　submerged　by　the　severe　fault　features　and　strong　background　noise,　which　easily　lead　to　a　missed　diagnosis.　To　solve　this　problem,　a　novel　diagnosis　method　combining　multi-symplectic　geometry　mode　decomposition　(MSGMD)　and　multipoint　optimal　minimum　entropy　deconvolution　adjusted　(MOMEDA)　is　proposed　for　gearbox　compound　fault　in　this　paper.　Specifically,　different　fault　components　are　separated　by　an　improved　symplectic　geometry　mode　decomposition　(SGMD),　namely　the　MSGMD　method.　The　weak　fault　features　are　enhanced　by　the　MOMEDA.　In　the　process　of　research,　a　new　scheme　of　selecting　the　key　parameters　for　MOMEDA　is　proposed,　which　is　a　key　step　in　the　practical　application　of　MOMEDA.　Compared　with　SGMD,　the　proposed　MSGMD　has　two　main　improvements,　including　suppressing　mode　mixing　and　preventing　the　generation　of　pseudo-components.　Compared　with　the　original　method　of　selecting　parameters　based　on　multipoint　kurtosis,　the　proposed　MOMEDA　parameter-selecting　scheme　has　the　merits　of　higher　accuracy　and　greater　precision.　The　analysis　results　of　two　cases,　of　simulation　and　an　experiment　signal,　reveal　that　the　MSGMD-MOMEDA　method　can　accurately　diagnose　gearbox　compound　fault　even　under　strong　background　noise.