The effects of radiative-trapping and fluorescence-concentration quenching on the emission spectra and fluorescence lifetimes of ${\mathrm{Yb}}^{3+}$ -doped $\mathrm{Y}{\mathrm{Al}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$ crystals with a series of ${\mathrm{Yb}}^{3+}$ concentrations were studied. The shift of barycenters in emission spectra, $\Delta \lambda$ , was proposed as an appraisement of the radiative-trapping effect on the spectra, and an empirical relation between $\Delta \lambda$ and ${\mathrm{Yb}}^{3+}$ concentration in the $\mathrm{Yb}:\mathrm{Y}{\mathrm{Al}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$ crystals was deduced. The model of excitation random walk was used to analyze the effects of radiative trapping and concentration quenching on the fluorescence lifetimes. The relation between fluorescence lifetime and ${\mathrm{Yb}}^{3+}$ concentration was obtained.