Epsilon-negative (ENG) and mu-negative (MNG) materials are fabricated by using transmission line (TL) approach, the electromagnetic tunneling properties of the bilayer structures with ENG-MNG materials are experimentally investigated. The results indicate that the two kinds of single negative materials do not support electromagnetic propagation modes, whereas the completely tunneling phenomenon occurs in the ENG-MNG pairs under special conditions when the average permittivity or average permeability equals zero respectively. Furthermore, the tunneling modes are insensitive to the scale length. Exponential amplification of the evanescent wave is also experimentally observed by simulating and measuring the electric field distributions in ENG-MNG structures at the tunneling frequency.