In order to improve the flexibility of the control to far-field directivity, the double butterfly-shap silver nanostructure optical antenna is put forword. The influence of the far-field directivity caused by different structures and sizes is researched based on finite difference time domain method. The research demonstrates that, because of the exist of localized surface plasmon, far- field pattern shows a significant side lobe when the dipole is placed beneath the structure vertically. The increase of length is the key factory to make the side lobe appears in the farfiled pattern. The decrease of the gap between antenna arms can make the side lobe and the main lobe gain increase in the far-field pattern. The increase in antenna thickness causes a side lobe in the far-field pattern and the main lobe gain first increases then decreases. The results show that double butterfly-shap silver nano optical antenna can change the radiation directivity of the coupling dipole source.