We present a numerical investigation of efficient generation of second harmonic from a kind of nonlinear magnetic metamaterial composite. The analysis is focused on a struc- ture consisting of periodic arrays of paired thin silver strips with second-order nonlinear material filled in the gap. The sandwich shaped periodic structure exhibits remarkable advantage in the generation of second harmonic signal. We, first, make an introduction to this sandwich structure, summarize the linear resonant properties and then investigate the wavelength dependence of the field enhancement in the gap. Next, we analyze about second-harmonic generation (SHG) from composite structure doping with isotropic nonlinear material by comparing with that from single layer nonlinear material and several other conditions. The results figure out that the magnetic resonance property of this nonlinear metamaterial composite makes a great contribution to the energy localization and gives rise to strong inhomogeneous field inside the gap. As a result, the strength of SHG is almost two orders larger than that of a pure nonlinear layer with compa- rable dimensions. Finally, we change the material property from isotropic to anisotropic, and investigate the impact combining with field enhancement, field profiles and linear and nonlinear polarization considerations, showing that most of the fundamental-harmonic electric field in the gap polarize along y direction, which is the power giving rise to the second-harmonic generation of the composite. This work leads to deeper understanding of singular nonlinear response in metamaterials.