In　this　paper,　we　introduce　the　notion　of　approximately　dual　Hilbert-Schmidt　frames.　We　establish　the　links　between　approximately　dual　Hilbert-Schmidt　frames　and　dual　Hilbert-Schmidt　frames,　and　between　approximately　dual　Hilbert-Schmidt　frames　and　approximately　dual　frames;　obtain　a　procedure　to　construct　approximately　dual　Hilbert-Schmidt　frames;　prove　that　(canonical)　dual　Hilbert-Schmidt　frames　inherit　the　stability　of　their　underlying　Hilbert-Schmidt　frames.　A　perturbation　theorem　of　approximately　dual　Hilbert-Schmidt　frames　is　also　presented.