This paper examines the growth of dark matter and dark energy perturbations within a non-canonical scalar field model characterized by an exponential potential. Through dynamical system analysis, we identify critical points and track the background evolution of a spatially flat FLRW universe dominated by dark energy and pressureless dark matter. We systematically derive key cosmological quantities, including the Hubble parameter, deceleration parameter, density parameters, and the scalar field’s equation of state, and explore their dependence on model parameters. Within the linear perturbation framework, employing the pseudo-Newtonian formalism, we compute the growth factor of matter density perturbations. To investigate the non-linear regime of structure formation, we employ the spherical collapse model and derive its key parameters. Building on these findings, we compute the function 𝑓(𝑧)𝜎8(𝑧) and the relative number density of halo objects exceeding a given mass threshold. Our results indicate that non-canonical scalar field models can effectively account for both background cosmic evolution and the growth of structure, offering potential insights into observational constraints and large-scale dynamics.
