Within the framework of DBI non-canonical scalar field model of dark energy, we study the growth of dark matter perturbations in both the 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. In the linear regime, we use the Pseudo-Newtonian formalism to obtain the growth factor of dark matter perturbations and conclude that for smaller $c_s$ (or $\tilde{f_0} \equiv f_0 H_0^2/M_P^2$), the growth factor of dark matter is smaller for clustering DBI model compared to the homogeneous one. 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 models. Finally, with the help of spherical collapse parameters we calculate 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 the higher-mass halos at high redshift.
