Motivated by the latest discovery of doubly-charmed tetraquark T + cc by LHCb collaboration, we have been studied the magnetic moments of the possible doubly-heavy pentaquark states with quantum numbers J P = 1/2 − and J P = 3/2 − within the light-cone sum rules method. In the analysis, these possible pentaquark states are considered in diquark-diquark-antiquark structure. The magnetic moments of hadrons encode helpful details about the distributions of the charge and magnetization inside the hadrons, which help us to figure out their geometric configurations. As a by product, the electric quadrupole and magnetic octupole moments of the spin-3/2 doubly-heavy pentaquark states are also extracted. These values show a non-spherical charge distribution. It will be interesting and useful to examine the magnetic moments of these possible doubly-heavy pentaquark states with different theoretical approaches.