  Recently, a novel equation of state (EoS) parameter for dark energy has been
introduced which deals with a special mathematical function, known as the
Lambert$W$ function. In this paper, we study the effect on the growth of
perturbations for the Lambert$W$ dark energy model. We perform the analysis for
two different approaches. In the first case we consider the universe to be
filled with two different fluid components, namely, the baryonic matter
component and the Lambert$W$ dark energy component, while in the second case we
consider that there is a single fluid component in the universe whose equation
of state parameter is described by the Lambert$W$ function. We then compare the
growth rates of Lambert$W$ model with that for a standard $\Lambda$CDM model as
well as the CPL model. Our results indicate that the presence of Lambert$W$
dynamical dark energy sector changes the growth rate and affects the matter
fluctuations in the universe to a great extent.
