Carbon-based superlattices represent a novel class of quantum metamaterials having promising prospects. Here, we show the first fabrication of folded bilayer-bilayer graphene (fBBLG)/hexagonal boron nitride (hBN) superlattices. In the transport properties at low temperatures, satellite peaks are observed due to the crystallographic angle alignment of fBBLG and hBN. The peculiar resistance peaks appear away from the charge neutrality point and the hBN-induced satellites, which may be signatures of possible competing orders. Our results suggest the emergence of a unique electronic band-structure in the fBBLG, providing a way for investigating the correlated electron phenomena by performing energy-band engineering with superlattice structures.