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In the framework of a non-relativistic quark model, the mass spectra of the ground and excited states of doubly heavy Ξ and Ω baryons are calculated. We estimate the mass difference between the Ω and corresponding Ξ baryons as MΩ−MΞ≃178 MeV for all the states containing cc,bc, or bb quarks. A simple form of the universal Isgur-Wise function, as the transition form factor between the doubly heavy baryons, is introduced. Working in the close-to-zero recoil limit, we investigate the b→c semileptonic decay widths and branching fractions of the doubly heavy baryons. The obtained results are compared with other theoretical predictions.