The nonlinear optical response in graphene is finding increasing applications in nanophotonic devices. The activation and enhancement of second harmonic generation (SHG) in graphene, which is generally forbidden in monolayer and AB-stacked bilayer graphene due to their centrosymmetry, is of urgent need for nanophotonic applications. Here, we present a comprehensive study of SHG performance of twisted multilayer graphene structures based on stacking engineering. It is found that the modulation of in-plane and out-of-plane SHG susceptibility components by stacking few-layer graphene is essential in producing giant SHG response in twisted multilayer graphene. Giant SHG intensity in twisted multilayer graphene is observed, reaching nearly 10 times that of monolayer MoS2 under 1064 nm excitation, which significantly outperformed graphene structures reported to date. Our findings present a facile and effective approach to enhance SHG in graphene structures, showing promise for future application of graphene in second harmonic nanophotonic devices as well as prospects for the study of SHG among two-dimensional (2D) structures in general.