  The nuclear spin relaxation time $T_1$ is calculated taking account of the
contributions from orbital currents of Dirac electrons. We consider a simple
model of non-interacting Dirac electron gas in the three-dimensional bulk
system. The obtained result shows $T^3$ dependence of $1/T_1$ at temperatures
$T$ above the energy gap. This temperature dependence agrees qualitatively with
the recent $\beta$-NMR experiment on the bulk of the topological insulator
$\mathrm{Bi}_{0.9}\mathrm{Sb}_{0.1}$.
