This　letter　investigates　a　joint　antenna　selection　(AS)　problem　for　a　MIMO　cognitive　radio-inspired　non-orthogonal　multiple　access　network.　In　particular,　a　new　computationally　efficient　joint　AS　algorithm,　namely　subset-based　joint　AS　(SJ-AS),　is　proposed　to　maximize　the　signal-to-noise　ratio　of　the　secondary　user　under　the　condition　that　the　quality　of　service　of　the　primary　user　is　satisfied.　The　asymptotic　closed-form　expression　of　the　outage　performance　for　SJ-AS　is　derived,　and　the　minimal　outage　probability　achieved　by　SJ-AS　among　all　possible　joint　AS　schemes　is　proved.　The　provided　numerical　results　demonstrate　the　superior　performance　of　the　proposed　scheme.