In this study， we propose a type of photonic crystal fiber with a silicon nanocrystal core exhibiting improved nonlinearity and reduced dispersion slope and fabrication difficulty. The core and cladding air holes are round. The effects of the core diameter， the diameter of the air holes in the cladding， and the lattice constant on dispersion and nonlinearity are investigated using the plane wave expansion method. A photonic crystal fiber with high nonlinearity and low dispersion slope can be obtained through optimization when considering a zero-dispersion wavelength of 1550 nm. Here， the dispersion slope of fiber at 1550 nm wavelength is as low as 0.251 ps·nm^-2·km^-1， whereas the nonlinear coefficient is as high as 1.0×10⁵ W^-1·km^-1. Further， the confinement loss is 0.39 dB/km. The structure of the photonic crystal fiber is simple and its fabrication is easy. In addition， it can maintain good performance even in the presence of small process errors.