We have designed a low-loss magnetic metamaterial with double-fishnet structures of silver and gold operating at near-infrared wavelength. A Particle swarm optimization algorithm was employed to optimize the geometry dimensions of Ag-dielectric-Au unit cell. The Ag-Au bimetallic fishnet produces a maximum figure of merit value of 21, transmission as high as 62%, moderate negative permeability Re(μ) of -0.5, and Re(n) of -1 at 1463 nm. The negative permeability Re(μ) reaches minimum value of -5 at 1573 nm, where the antisymmetric charge distribution in fishnet metamaterials was observed. The antisymmetric plasmonic resonance at 1573 nm is a mixed mode of asymmetric magnetic dipole and symmetric electrical quadrupole in Ag-MgF -Au fishnet structures.