In this paper, the mass spectra are obtained for doubly heavy baryons, namely, + cc , ++ cc , − bb , 0 bb , 0 bc and + bc . These baryons consist of two heavy quarks (cc, bb, and bc) with a light (d or u) quark. The ground, radial, and orbital states are calculated in the framework of the hypercentral constituent quark model with Coulomb plus linear potential. Our results are also compared with other predictions, thus, the average possible range of excited states masses of these baryons can be determined. The study of the Regge trajectories is performed in (n, M 2 ) and (J , M 2 ) planes and their slopes and intercepts are also determined. Lastly, the ground state magnetic moments of these doubly heavy baryons are also calculated.