In this paper we consider classical strings propagating in γ-deformed AdS_3×S~3 backgrounds generatedby TsT transformation on the AdS3 sector,which is described as the group manifold SL(2,R),then we prove that theU(1) currents of strings with the twisted boundary conditions are equal to those in v-deformed backgrounds.Using TsTtransformation,we can derive the local Lax connection and the monodromy matrix in 7-deformed backgrounds with thespectral parameter,which ensures the classical integrability of the string theories. In this paper we consider classical strings propagating in γ-deformed AdS_3 × S ~ 3 backgrounds generatedby TsT transformation on the AdS3 sector, which is described as the group manifold SL (2, R), then we prove that theU (1) currents of strings with the twisted boundary conditions are equal to those in v-deformed backgrounds.Since TsTransformation, we can derive the local Lax connection and the monodromy matrix in 7-deformed backgrounds with the spectral parameter, which ensures the classical integrability of the string theories.