With the demanding requirements for light source, light emitting diodes (LED) attracts more and more attention because of its inherent advantages such as low power consumption, high reliability and longevity. However, there are two disadvantages for LED, one is the low light extraction efficiency resulting from the total internal reflection, and the other is the relative large scattered angle. In order to improve the light extraction efficiency and collimate the out-coupling light, a sub-micron Fresnel lens array is introduced and investigated in this paper. The focal length of the proposed Fresnel lens is 3μm and the minimum width of the outmost ring is about 150nm. To calculate and analyze the light extraction efficiency and the scattered angle of LED with such Fresnel lens array structure, we optimize the parameters of the Fresnel lens, such as the depth of the Fresnel lens array structure and the thickness of the p-type gallium nitride layer by using the finite difference time domain method (FDTD). By comparing the discussed patterned GaN-based LED with that traditional flat LEDs, it can be found that significant enhancement factor of the light extraction efficiency, which is improved by 3.5 times, can be obtained and the scattered angle at half maximum can be decreased 50° from 60° with this novel Fresnel lens structure. It will be expected that the proposed sub-micron structure can find wide applications in LEDs industry.