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Nonlinear characteristics of fused silica, solid-core photonic crystal fibers (PCFs) with a square array of air holes are studied numerically. We present a novel design that emphasizes the difference in air hole diameters in the photonic cladding. These PCFs have the advantages of flat dispersion, high nonlinearity, and low attenuation. Based on simulation results, three optimal structures, denoted #F1, #F2, and #F3, having anomalous and all-normal dispersions in the near-infrared range are selected to investigate characteristic properties at the pump wavelength. Such PCFs open up many possibilities for nonlinear optical applications, especially supercontinuum generation.