In this paper, a photonic crystal fiber (PCF) with a dispersion-engineered and high nonlinear coefficient has been designed for supercontinuum generation (SCG) and frequency comb generation (FCG). The proposed PCF has a Si3N4 rod in the core. This rod provides more optical confinement in the core by increasing the refractive index of the core.This high confinement reduces the effective mode area of PCF and thus increases the nonlinear coefficient. The effective mod area and the nonlinear coefficient are obtained as 0.814 μm2 and 25 W-1m-1, respectively. By varying different parameters for dispersion engineering, a suitable dispersion profile for the structure has been obtained so that the proposed PCF has two zero dispersion wavelengths (ZDWs) at 900 nm and 1 590 nm. By injecting a pumping with power of 1 kW and duration of 50 fs at a wavelength of 1 555 nm to the designed PCF with a length of 4 mm, the output spectrum is broadened in the range from 800 nm to 3 500 nm. For FCG by the four-wave mixing (FWM) method,phase matching conditions must be provided, and for that, the pumped wavelength must be in the anomalous dispersion regime and near ZDW. As a result, two continuous wave lasers pumping at the wavelengths of 1 551 nm and 1 558 nm have been injected into the PCF and optical frequency combs (OFCs) with a pulse width of 1 nm and a free spectral range of 7 nm has been obtained.