  We employ the holographic approach to study the thermalization in the
quenched strongly-coupled field theories with very general anisotropic scalings
including Lifshitz and hyperscaling violating fixed points. The holographic
dual is a Vaidya-like time-dependent geometry where the asymptotic metric has
general anisotropic scaling isometries. We find the Ryu-Takanayagi extremal
surface and use it to calculate the time-dependent entanglement entropy between
a strip region with width $2R$ and its outside region. In the special case with
an isotropic metric, we also explore the entanglement entropy for a spherical
region of radius $R$. The growth of the entanglement entropy characterizes the
thermalization rate after a quench. We study the thermalization process in the
early times and late times in both large $R$ and small $R$ limits. The allowed
scaling parameter regions are constrained by the null energy conditions as well
as the condition for the existence of the Ryu-Takanayagi extremal surfaces.
This generalizes the previous works on this subject. All obtained results can
be compared with experiments and other methods of probing thermalization.
