The present invention relates to a method for differentiating mesenchymal stem cells and culturing chondrocytes using a fibrin/HA(hyaluronate) composite whose biocompatibility and durability are enhanced, and a therapeutic composition containing the fibrin/HA composite, and more particularly, to a method for culturing chondrocytes and differentiating mesenchymal stem cells into chondrocytes using an alginate-coated fibrin/HA composite gel and a composition for treating a cartilage disease and a composition for treating a disc disease using a fibrin/HA composite scaffold containing a fibrin degradation inhibitor. According to the present invention, disadvantages of the traditional fibrin/HA composite being reduced in size and easily degraded in a short time period during culture were overcome, so that cells can be cultured in a more stable environment. The treatment composition according to the present invention has superior biocompatibility and biodegradability and thus it can be used for effective treatment for cartilage diseases, and it can regenerate the nuclei pulposi of a new intervertebral disk unlike currently used surgical treatment of degenerative intervertebral disk disease, so that it is expected that fundamental treatment of disc diseases can be achieved.