We propose, analyze and optimize a two-dimensional conical photonic crystal geometry to enhance light extraction from a high refractive index material, such as an inorganic scintillator. The conical geometry suppresses Fresnel reflections at an optical interface due to adiabatic impedance matching from a gradient index effect. The periodic array of cone structures with a pitch larger than the wavelength of light diffracts light into higher-order modes with different propagating angles, enabling certain photons to overcome total internal reflection (TIR). The numerical simulation shows simultaneous light yield gains relative to a flat surface both below and above the critical angle and how key parameters affect the light extraction efficiency. Our optimized design provides a 46% gain in light yield when the conical photonic crystals are coated on an LSO (cerium-doped lutetium oxyorthosilicate) scintillator.