  In this work, we perform a systematic study of the mass spectra, the root
mean square(r.m.s.) radii and the radial density distributions of the doubly
charmed baryons $\Xi_{cc}$ and $\Omega_{cc}$. The calculations are carried out
in the frame work of Godfrey-Isgur (GI) relativized quark model, where the
baryon is regarded as a real three-body system of quarks. Our results show that
the excited energy of doubly charmed baryon with $\rho$-mode is lower than
those of the $\lambda$-mode and $\lambda$-$\rho$ mixing mode, which indicates
that the lowest state is dominated by the $\rho$-mode. According to this
conclusion, we systematically investigate the mass spectra, the r.m.s. radii of
the ground and excited states($1S\sim4S$, $1P\sim4P$, $1D\sim4D$, $1F\sim4F$
and $1G\sim4G$) with $\rho$-mode. Using the wave functions obtained from quark
model, we also study the radial density distributions. Finally, with the
predicated mass spectra, the Regge trajectories of $\Xi_{cc}$ and $\Omega_{cc}$
in the ($J$,$M^{2}$) plane are constructed, and the slopes, intercepts are
determined by linear fitting. It is found that model predicted masses fit
nicely to the constructed Regge trajectories.
