In　this　study,　a　Back　Propagation　(BP)　neural　network　algorithm　based　on　Genetic　Algorithm　(GA)　optimization　is　proposed　to　plan　and　optimize　the　trajectory　of　a　redundant　robotic　arm　for　the　upper　limb　rehabilitation　of　patients.　The　feasibility　of　the　trajectory　was　verified　by　numerical　simulations.　First,　the　collected　dataset　was　used　to　train　the　BP　neural　network　optimized　by　the　GA.　Subsequently,　the　critical　points　designated　by　the　rehabilitation　physician　for　the　upper　limb　rehabilitation　were　used　as　interpolation　points　for　cubic　B-spline　interpolation　to　plan　the　motion　trajectory.　The　GA　optimized　the　planned　trajectory　with　the　goal　of　time　minimization,　and　the　feasibility　of　the　optimized　trajectory　was　analyzed　with　MATLAB　simulations.　The　planned　trajectory　was　smooth　and　continuous.　There　was　no　abrupt　change　in　location　or　speed.　Finally,　simulations　revealed　that　the　optimized　trajectory　reduced　the　motion　time　and　increased　the　motion　speed　between　two　adjacent　critical　points　which　improved　the　rehabilitation　effect　and　can　be　applied　to　patients　with　different　needs,　which　has　high　application　value.