Light extraction analysis of GaN-based light-emitting diodes (LEDs) with Monte Carlo ray tracing is presented. To obtain high light extraction efficiency, periodic structures introduced on the top surface and/or on the substrate of various types of LED are simulated, including wire bonding, flip chip and Thin GaN. Micro pyramid array with an apex angle from 20o to 70o is shown to effectively improve the light extraction efficiency. In addition, for an LED encapsulated within an epoxy lens, the patterned substrate with pyramid array is found to be a more effective way to increase light extraction efficiency than the surface texture.