  In this paper, we will analyse the holographic complexity for time-dependent
asymptotically $AdS$ geometries. We will first use a covariant zero mean
curvature slicing of the time-dependent bulk geometries, and then use this
co-dimension one spacelike slice of the bulk spacetime to define a co-dimension
two minimal surface. The time-dependent holographic complexity will be defined
using the volume enclosed by this minimal surface. This time-dependent
holographic complexity will reduce to the usual holographic complexity for
static geometries. We will analyse the time-dependence as a perturbation of the
asymptotically $AdS$ geometries. Thus, we will obtain time-dependent
asymptotically $AdS$ geometries, and we will calculate the holographic
complexity for such a time-dependent geometries.
