Disclosed is a therapeutic method including administering a TIM-3 antibody or its TIM-3 binding fragment to a subject who is suspected to be suffering from blood tumor and in whom TIM-3 has been expressed in a Lin(−)CD34(+)CD38(−) cell fraction of bone marrow or peripheral blood or a subject who has been received any treatment for blood tumor. Conceived diseases include those diseases which can be treated through the binding or targeting of the TIM-3 antibody or its TIM-3 binding fragment to blood tumor cells (AML cells, CML cells, MDS cells, ALL cells, CLL cells, multiple myeloma cells, etc.), helper T cell (e.g., Th1 cells, Th17 cells), and antigen-presenting cells (e.g., dendritic cells, monocytes, macrophages, and cells resembling to the aforementioned cells (hepatic stellate cells, osteoclasts, microglial cells, intraepidermal macrophages, dust cells (alveolar macrophages), etc)).