We show that resonant tunneling of electromagnetic (EM) fields can occur through a six-layer structure con-sisting of two pairs of bilayer slabs: one being an epsilon-negative layer and the other being a mu-negative layer with a double-positive (DPS) medium and air. This type of tunneling is accompanied by high-magnetic field. The Poynting vector distributions and the material dissipation are studied. Our results demonstrate that the EM field in the structure is controlled flexibly by single-negative media and DPS slab. Therefore, this structure has potential applications in wireless energy transfer.