Using the noncanonical 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 inmagnitude with increasing the value of the scalar field. A special solution of the nonlinear field equations of 𝜙 that has time dependency as fixed point is obtained. The fixed point relies on the noncanonical termof action and 𝛾-parameter; this parameter appeared in energy density of scalar field redshift. By means of such fixed point the different eigenvalues of the equation of motion will be obtained. In different epochs in the evolution of the Universe for different values of 𝑞 and 𝑛, the potentials as a function of scalar field are attained.The behavior of baryonic perturbations in linear perturbation scenario as a considerable amount of energy density of scalar field at low redshifts prevents the growth of perturbations in the ordinarymatter fluid.The energy density in the scalar field is not appreciably perturbed by nonrelativistic gravitational fields, in either the radiation or matter dominant or scalar field dominated epoch.