Disclosed is a therapeutic method comprising administering a TIM-3 antibody 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. Also disclosed is a composition for preventing or treating blood tumor, which comprises a TIM-3 antibody as an active ingredient. Conceived diseases include those diseases which can be treated through the binding or targeting of the TIM-3 antibody 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)), all of which are capable of expressing TIM-3. The diseases for which the therapeutic use is to be examined include blood diseases in which the expression of TIM-3 is observed in bone marrow or peripheral blood, particularly blood tumor.