  Within the framework of DBI non-canonical scalar field model of dark energy,
we study the growth of dark matter perturbations in the both linear and
non-linear regimes. In our DBI model, we consider the anti-de Sitter warp
factor $f(\phi)=f_0\, \phi^{-4}$ with constant $f_0>0$ and assume the DBI dark
energy to be clustered and its sound speed $c_s$ to be constant. For a
spatially flat FRW universe filled with pressureless dark matter and DBI dark
energy, we first obtain the evolutionary behaviors of the background
quantities. Our results show that in our DBI model, the universe starts from a
matter dominated epoch and approaches to the de Sitter universe at late times,
as expected. Also the DBI potential behaves like the power law one
$V(\phi)\propto \phi^n$.
  In addition, we use the Pseudo-Newtonian formalism to obtain the growth
factor of dark matter perturbations in the linear regime. We conclude that for
smaller $c_s$ (or $f_0$), the growth factor of dark matter is smaller for
clustering DBI model compared to the homogeneous one. In the following, in the
non-linear regime based on the spherical collapse model, we obtain the linear
overdensity $\delta_c(z_c)$, the virial overdensity $\Delta_{\rm vir}(z_c)$,
overdensity at the turn around $\zeta(z_c)$ and the rate of expansion of
collapsed region $h_{\rm ta}(z)$. We point out that for the smaller $c_s$ (or
$\tilde{f}_0$), the values of $\delta_c(z_c)$, $\Delta_{\rm vir}(z_c)$,
$\zeta(z_c)$ and $h_{\rm ta}(z)$ in non-clustering DBI models deviate more than
the $\Lambda$CDM compared to the clustering DBI. Finally, with the help of
spherical collapse parameters we calculated the relative number density of halo
objects above a given mass and conclude that the differences between clustering
and homogeneous DBI models are more pronounced for higher-mass halos at high
redshift.
