We study the mass spectra and radiative decays of doubly heavy baryons within the diquark picture in a relativized quark model. The mass of the JP=1/2+ Ξcc ground state is predicted to be 3606 MeV, which is consistent with the mass of Ξcc++(3621) newly observed by the LHCb Collaboration. The predicted mass gap between two S-wave states, Ξcc* (JP=3/2+) and Ξcc (JP=1/2+), is 69 MeV. Furthermore, the radiative transitions of doubly heavy baryons are also estimated by using the realistic wave functions obtained from relativized quark model. The radiative decay widths of Ξcc*++→Ξcc++γ and Ξcc*+→Ξcc+γ are predicted to be about 7 and 4 keV, respectively. These predictions of doubly heavy baryons can provide helpful information for future experimental searches.