Stimulated by the newly reported doubly-charmed tetraquark state T + cc by LHCb, we carry out a systematic investigation of the S -wave interactions between the charmed meson (D, D * ) in H-doublet and the charmed meson (D 1 , D *2 ) in T -doublet by adopting the one-boson-exchange model. Both the S -D wave mixing effect and the coupled channel effect are taken into account. By performing a quantitative calculation, we suggest that the S -wave D * D 1 states with I(J P ) = 0(0 − , 1 − ) and the S -wave D * D * 2 state with I(J P ) = 0(1 − ) should be viewed as the most promising candidates of the doubly-charmed molecular tetraquark states, and the S -wave DD 1 state with I(J P ) = 0(1 − ), the S -wave DD * 2 state with I(J P ) = 0(2 − ), and the S -wave D * D * 2 state with I(J P ) = 0(2 − ) are the possible doubly-charmed molecular tetraquark candidates. With the accumulation of experimental data at Run III and after High-Luminosity-LHC upgrade, these predicted doubly-charmed molecular tetraquark states can be accessible at LHCb in the near future.