In this article, we have investigated the enhanced second-harmonic generation (SHG) from Fanolike resonance in an asymmetric homodimer of gold elliptical nanodisks using a three-dimensional finite element method. We have found that the broken symmetry will cause Fanolike resonances in the extinction spectrum, resulting in the enhancement of SHG efficiency. When one of the gold elliptical nanodisks rotates, the SHG efficiency increases first and then decreases. In addition, we have also shown that the SHG signal blue-shifts with the reduction of efficiency when the separation between two nanodisks increases. Furthermore, when the nanodisks become thicker, the SHG signal also blue-shifts with the increase of efficiency. The SHG signal from this simple plasmonic structure with high efficiency and tunability may pave a way toward practical applications in sensing and generating a new light source.