  Topological insulators have been extended to higher-order versions that
possess topological hinge or corner states in lower dimensions. However, their
robustness against disorder is still unclear. Here, we theoretically
investigate the phase transitions of three-dimensional (3D) chiral second-order
topological insulator (SOTI) in the presence of disorders. Our results show
that, by increasing disorder strength, the nonzero densities of states of side
surface and bulk emerge at critical disorder strengths of $W_{S}$ and $W_{B}$,
respectively. The spectral function indicates that the bulk gap is only closed
at one of the $R_{4z}\mathcal{T}$-invariant points, i.e., $\Gamma_{3}$. The
closing of side surface gap or bulk gap is ascribed to the significant decrease
of the elastic mean free time of quasi-particles. Because of the localization
of side surface states, we find that the 3D chiral SOTI is robust at an
averaged quantized conductance of $2e^{2}/h$ with disorder strength up to
$W_{B}$. When the disorder strength is beyond $W_{B}$, the 3D chiral SOTI is
then successively driven into two phases, i.e., diffusive metallic phase and
Anderson insulating phase. Furthermore, an averaged conductance plateau of
$e^{2}/h$ emerges in the diffusive metallic phase.
