  The dynamical spin susceptibility in the new-structure-type iron-based
superconductor CaKFe$_4$As$_4$ was investigated by using a combination of
inelastic neutron scattering (INS) measurements and random phase approximation
(RPA) calculations. Powder INS measurements show that the spin resonance at
$Q_\text{res}=1.17(1)$~$\text{\AA}^{-1}$, corresponding to the $(\pi,\pi)$
nesting wave vector in tetragonal notation, evolves below $T_\text{c}$. The
characteristic energy of the spin resonance $E_\text{res}=12.5$~meV is smaller
than twice the size of the superconducting gap ($2\Delta$). The broad energy
feature of the dynamical susceptibility of the spin resonance can be explained
by the RPA calculations, in which the different superconducting gaps on
different Fermi surfaces are taken into account. Our INS and PRA studies
demonstrate that the superconducting pairing nature in CaKFe$_4$As$_4$ is the
$s_\pm$ symmetry.
