  A high density CaKFe$_4$As$_4$ bulk sample was successfully synthesized using
a spark plasma sintering (SPS) technique. The density of the synthesized sample
was 5.02 g cm$^{-3}$, corresponding to 96.2% of the theoretical density of
CaKFe$_4$As$_4$. Moreover, a reasonably high Vickers hardness of 1 GPa was
measured. The electrical resistivity of the SPS bulk sample was as low as
approximately 600 $\mu\Omega$ cm at 300 K, which is smaller than that of the
ordinary sintered polycrystalline sample by nearly one order of magnitude, and
exhibited a sharp superconducting transition, with the transition width
$\Delta\textit{T}_c$ less than 2 K, indicating an improved grain connectivity.
The critical current density of the SPS bulk sample, as calculated from the
magnetization hysteresis loops (magnetic $\textit{J}_c$), reached 18 kA
cm$^{-2}$ at 4.2 K under 5 T, which is the highest among the iron-based
superconductor polycrystalline samples reported thus far.
