Experimental tests on human corneas reveal distinguished reinforcing collagen lamellar structures that may be well described by a structural constitutive model considering distributed collagen fibril orientations along the superior-inferior and the nasal-temporal meridians. A proper interplay between the material structure and the geometry guarantees the refractive function and defines the refractive properties of the cornea. We propose a three-dimensional computational model for the human cornea that is able to provide the refractive power by analyzing the structural mechanical response with the nonlinear regime and the effect the intraocular pressure has. For an assigned unloaded geometry we show how the distribution of the von Mises stress at the top surface of the cornea and through the corneal thickness and the refractive power depend on the material properties and the fibril dispersion. We conclude that a model for the human cornea must not disregard the peculiar collagen fibrillar structure, which equips the cornea with the unique biophysical, mechanical, and optical properties.