  Motivated by great progresses in experiments in searching for the heavy
baryons, we systematically analyze the mass spectra and root mean square radius
of single heavy baryons $\Lambda_{Q}$, $\Sigma_{Q}$ and $\Omega_{Q}$. The
calculations of the mass spectra are carried out in the frame work of
Godfrey-Isgur (GI) relativized quark model, where the baryon is regarded as a
three-body system of quarks. Our results show that the mass of single heavy
baryon with $\lambda$-mode is lower than those of the $\rho$-mode and
$\lambda$-$\rho$ mixing mode, which indicates that the lowest state is
dominated by the $\lambda$-mode. Basing on this research, we systematically
calculate the mass spectra and the root mean square radius of the baryons with
$\lambda$ excited mode. With these predicated mass spectra, the Regge
trajectories in the ($J$,$M^{2}$) plane are constructed, and the slopes,
intercepts of the Regge trajectories are obtained by linear fitting. It is
found that all available experimental data are well reproduced by model
predictions and fit nicely to the constructed Regge trajectories.
