  The LaBr$_3$(Ce) detector has attracted much attention in recent years for
its superior characteristics to other scintillating materials in terms of
resolution and efficiency. However, it has relatively high intrinsic radiation
background due to the naturally occurring radioisotope in lanthanum, actinium
and their daughter nuclei. This limits its applications in low counting rate
experiments. In this paper, we identified the radioactive isotopes in the
$\phi3''\times 3''$ Saint-Gobain B380 detector by a coincidence measurement
using a Clover detector in a low-background shielding system. Moreover, we
carried out a Geant4 simulation to the experimental spectra to evaluate the
activities of the main internal radiation components. % by means of the
$\alpha$, $\gamma$ and $\beta$ decays from the $^{138}$La and $^{227}$Ac. The
activity of radiation background of B380 is determined to be 1.480 (69)
Bq/cm$^3$, the main sources of which include $^{138}$La of 1.425 (59)
Bq/cm$^3$, $^{211}$Bi of 0.0136 (15) Bq/cm$^3$, $^{219}$Rn of 0.0125 (17)
Bq/cm$^3$, $^{223}$Ra of 0.0127 (14) Bq/cm$^3$, and $^{227}$Th of 0.0158 (22)
Bq/cm$^3$.
