Using the non-cononical model of scalar field, the cosmological consequences of a pervasive, self-interacting, homogeneous and rolling scalar field are studied. In this model, the scalar-field potential is "nonlinear" and decreases in magnitude by increasing the value of the scalar field. A special solution of the nonlinear field equations of $\phi$ that is a time dependent, fixed point is obtained. The fixed point relies on the non-cononical term of action and $q$- parameter which is appeared in energy density of scalar field red-shift. The behavior of baryonic perturbations in linear perturbation scenario a considerable amount of energy density of scalar-field at low red-shifts prevents the growth of perturbations in the ordinary matter fluid. The energy density in the scalar field is not appreciably perturbed by nonrelativistic gravitational fields, either in the radiation-dominated, matter-dominated, or scalar-field-dominated epochs.
