Low-dose　computed　tomography　(LDCT)　is　an　effective　approach　to　reduce　radiation　exposure　to　patients.　Lots　of　mottle　noise　and　streak　artifacts,　however,　are　introduced　to　the　reconstructed　image.　Current　weighted　nuclear　norm　minimization　(WNNM)　denoising　method　cannot　remove　the　streak　artifacts　in　LDCT　image　completely,　even　if　many　time-consuming　iterations　are　adopted.　In　this　paper,　an　effective　image　denoising　algorithm,　which　is　based　on　discriminative　weighted　nuclear　norm　minimization　(DWNNM),　is　proposed　to　improve　LDCT　image.　In　the　D-WNNM　method,　the　local　entropy　of　the　image　is　exploited　to　discriminate　streak　artifacts　from　tissue　structure,　and　to　tune　WNNM　weight　coefficients　adaptively.　Additionally,　a　preprocessed　image　is　used　to　improve　the　accuracy　of　block　matching,　and　the　total-variation　(TV)　algorithm　is　applied　to　further　reduce　the　residual　artifacts　in　the　recovered　image.　We　evaluate　the　D-WNNM　method　on　the　simulated　pelvis　phantom,　the　actual　thoracic　phantom,　and　the　clinical　thoracic　data,　and　compared　it　to　several　other　competitive　methods.　Experimental　results　show　that　the　proposed　approach　has　better　performance　in　both　artifacts　suppression　and　structure　preservation.　Particularly,　the　number　of　iterations　required　in　the　proposed　algorithm　is　substantially　reduced　(only　twice),　when　compared　with　that　required　in　the　WNNM　method　(at　least　eight　iterations).