The near-field distribution of silver nanodisk optical antenna was calculated with Finite-Difference Time-Domain method. The influence to the far-field characteristics by different parameters such as the distance between nanodisk and dipole, thickness and radius of nanodisk, was discussed. The research demonstrated that when the dipole was placed vertically beneath the nanodisk, the variation of thickness or radius could lead to new radiation mode in the far-field pattern and give rise to the enhancement of directivity gain. Through the observation and analysis to near-field, it could be obtained that the new radiation mode was caused by the high order localized surface plasmon(LSP) mode. The optimization results pointed out that as the background material was set as GaN, for the sake of producing high order LSP mode, the suitable distance between nanodisk and dipole was 40 nm. Furthermore, in order to effectively support the high order LSP mode, the thickness and radius of nanodisk were at least 30 nm and 100 nm respectively. These results provided a theoretical reference to master the characteristics of nanodisk optical antenna as well as the practical application in optical devices.