Hilbert-Schmidt　frame　(HS-frame)　has　interested　some　mathematicians　in　recent　years,　which　is　more　general　than　g-frame.　This　paper　addresses　near　Riesz　and　Besselian　properties　of　HS-operator　sequences.　We　characterize　HS-frame　and　Riesz　properties　of　g-operator　sequences　using　their　DSI-sequences;　prove　that　an　HS-Riesz　basis　is　an　exact　HS-frame　while　the　converse　is　not　true,　and　an　arbitrary　HS-Riesz　frame　contains　an　HS-Riesz　basis;　and　present　the　connection　among　near　HS-Riesz　property,　Besselian　property　and　the　kernel　space　dimension　of　synthesis　operator　of　an　HS-operator　sequence.