Due　to　the　problem　of　a　small　amount　of　EEG　samples　and　relatively　high　dimensionality　of　electroencephalogram　(EEG)　features,　feature　selection　plays　an　essential　role　in　EEG-based　emotion　recognition.　However,　current　EEG-based　emotion　recognition　studies　utilize　a　problem　transformation　approach　to　transform　multi-dimension　emotional　labels　into　single-dimension　labels,　and　then　implement　commonly　used　single-label　feature　selection　methods　to　search　feature　subsets,　which　ignores　the　relations　between　different　emotional　dimensions.　To　tackle　the　problem,　we　propose　an　efficient　EEG　feature　selection　method　for　multi-dimension　emotion　recognition　(EFSMDER)　via　local　and　global　label　relevance.　First,　to　capture　the　local　label　correlations,　EFSMDER　implements　orthogonal　regression　to　map　the　original　EEG　feature　space　into　a　low-dimension　space.　Then,　it　employs　the　global　label　correlations　in　the　original　multi-dimension　emotional　label　space　to　effectively　construct　the　label　information　in　the　low-dimension　space.　With　the　aid　of　local　and　global　relevance　information,　EFSMDER　can　conduct　representational　EEG　feature　subset　selection.　Three　EEG　emotional　databases　with　multi-dimension　emotional　labels　were　used　for　performance　comparison　between　EFSMDER　and　fourteen　state-of-the-art　methods,　and　the　EFSMDER　method　achieves　the　best　multi-dimension　classification　accuracies　of　86.43,　84.80,　and　97.86　percent　on　the　DREAMER,　DEAP,　and　HDED　datasets,　respectively.