PROBLEM TO BE SOLVED: To provide therapeutic compositions that are effective against chronic myelogenous leukemia in a more fundamental way, although therapeutic compositions of the second and third generations more effective than imatinib are now under development to overcome the problem that imatinib is effective for chronic myelogenous leukemia, but continuous administration of imatinib results in acquired drug resistance.SOLUTION: A therapeutic composition of the invention for chronic myelogenous leukemia comprises a first pharmaceutical composition comprising at least one selected from imatinib, nilotinib, dasatinib, ponatinib and bafetinib to inhibit Bcr-Abl tyrosine kinase a second pharmaceutical composition to inhibit Met tyrosine kinase or a third pharmaceutical composition to inhibit MEK kinase, where the combination use of these compositions can overcome the drug resistance.SELECTED DRAWING: Figure 7