In　recent　years,　more　dictionary　learning　algorithms　have　been　proposed,　and　the　Lagrange　dual　method　achieves　better　performance.　It　is　an　optimization　algorithm　with　the　gradient　descent　methods,　and　therefore　it　is　inevitable　to　deal　with　the　step　size　problem.　In　this　paper,　we　first　introduced　the　Lagrange　dual　method　thoroughly,　and　then　the　step　size　problem　is　discussed　in　detail.　Next,　a　sparse　coding　dictionary　updating　algorithm　with　BB　method　is　proposed:　combined　with　the　two-point　step　size　method　(or　BB　method)　proposed　by　Barzilai　and　Borwein,　the　Lagrange　dual　method　is　applied　to　solve　the　problem　of　step　size　adjustment.　The　proposed　algorithm　is　superior　to　other　methods　in　many　data　sets　as　shown　by　the　experimental　results.　©　2018　IEEE.