The spectroscopic performance of Yb-doped calcium fluorapatite (Yb:FAP) was assessed by measuring polarization absorption spectra, polarization emission spectra and fluorescence lifetime. The emission cross section has been evaluated using the absorption cross section and principle of reciprocity. The π polarization absorption and emission cross sections of Yb3+ in FAP are found to be substantially larger than those of other Yb-doped media. Favorable spectroscopic parameters show that Yb:FAP crystal is more desirable for many diode-pumped solid state laser application with low- and medium-power in the near future.