By simulating the field distributions of two optical dipole antenna models with the finite-difference time-domain (FDTD) method, the variation regularity of their far-field radiation with their length increasing and the factors which can influence their far-field directivity are studied. The results show that the variation regularity of optical dipole antenna is analogous to that of classic symmetrical dipole antenna. But in the far-field directivity plot of optical dipole antenna, side-lobes occur much more quickly, owing to the existence of high-order localized surface plasmon modes. These results hold a significant promise of improving the performance of optical antennas.