The invention discloses 3-methyl-5,7-diphenyl-5H-thiazolo[3,2-a]pyrimidine-2-carboxamide derivatives shown in a formula I, or pharmaceutically acceptable hydrates or salts of the derivatives, i.e., stereoisomers or tautomers of the derivatives, wherein R1 and R2 in the formula I are respectively hydrogen, methyl, halogen, hydroxyl, methoxyl, acetyl, propionyl, nitro or alkoxy independently; R3 and R4 are independently selected from C1-C6 alkyl, or R3 and R4 form pyrrolyl, piperidinyl, morpholinyl, N-methylpiperazine and N-(4-bromophenyl piperazine) together with nitrogen atoms which are connected with the R3 and the R4. As vascular endothelial growth factor receptor tyrosine kinase inhibitors, the 3-methyl-5,7-diphenyl-5H-thiazolo [3,2-a]pyrimidine-2-carboxamide derivatives can be used for treating and preventing various cancers. The formula I is shown in the description.