  We theoretically study the Kondo screening of a spin-1/2 magnetic impurity in
the bulk of a type-II Weyl semimetal (WSM) by use of the variational wave
function method. We consider a type-II WSM model with two Weyl nodes located on
the $k_z$-axis, and the tilting of the Weyl cones are along the $k_x$
direction. Due to co-existing electron and hole pockets, the density of states
at the Fermi energy becomes finite, leading to a significant enhancement of
Kondo effect. Consequently, the magnetic impurity and the conduction electrons
always form a bound state, this behavior is distinct from that in the type-I
WSMs, where the bound state is only formed when the hybridization exceeds a
critical value. Meanwhile, the spin-orbit coupling and unique geometry of the
Fermi surface lead to strongly anisotropic Kondo screening cloud in coordinate
space. The tilting terms break the rotational symmetry of the type-II WSM about
the $k_z$-axis, but the system remains invariant under a combined
transformation $\mathcal{T}R^{y}(\pi)$, where $\mathcal{T}$ is the
time-reversal operation and $R^{y}(\pi)$ is the rotation about the $y$-axis by
$\pi$. Largely modified diagonal and off-diagonal components of the spin-spin
correlation function on three principal planes reflect this change in band
symmetry. Most saliently, the tilting terms trigger the emergence of non-zero
off-diagonal components of spin-spin correlation function on the $x$-$z$
principal plane.
