In this paper, we report the growth of nanostructured poly(p-xylylene) (PPX) films by oblique angle polymerization at various deposition angles. Additionally, a two-dimensional computational (Monte Carlo) model is implemented to study the nanostructured growth process. The morphology of the nanostructured polymer films are characterized by atomic force microscopy and scanning electron microscopy. Based on the experimental results, a competitive growth model is proposed and quantified in terms of column geometry (i.e., diameter and height), column spacing (i.e., periodicity), and column packing (i.e., number of columns per unit area). We show that the nanostructured polymer growth obeys a universal power-law scaling mechanism at various deposition angles. The computational model predicts similar nanostructured morphologies to the oblique angle polymerization obtained experimentally. Nanostructured polymer films may provide great advances in sensing and biomedical applications.