  We report the results of low-temperature thermal and magnetic measurements on
Ba$_3$CoNb$_2$O$_9$ powder, described as a uniform triangular-lattice
antiferromagnet (TLAF) with a fictitious spin-1/2. Ba$_3$CoNb$_2$O$_9$ is found
to undergo two-step antiferromagnetic transitions at $T_{\rm N1}=1.39~{\rm K}$
and $T_{\rm N2}=1.13~{\rm K}$. As the magnetic field is increased, both $T_{\rm
N1}$ and $T_{\rm N2}$ monotonically decrease. The magnetic field vs temperature
phase diagram indicates that the exchange interactions are nearly of the
Heisenberg type with weak easy-axis anisotropy and that the exchange
interaction between triangular lattices is crucial, in contrast to the case of
the quasi-two-dimensional TLAF Ba$_3$CoSb$_2$O$_9$ [Susuki {\it et al}., Phys.
Rev. Lett. \textbf{110}, 267201 (2013)].
