Topology photonic, a combination of topology physics and optics provides novel visions to the demonstration of theoretical physics and designs principles to new optical devices. Being a key tool to condensed matter physics, tight-binding model helps the development of topology physics. We found that by changing the background material from vacuum to an effective medium with negative permittivity in traditional photonic crystals, a one-to-one correspondence to tight-binding model can be found for this new type of photonic crystal. We show by numerical simulations the existence of edge states located at both the zigzag and bearded boundaries of a honeycomb-lattice photonic crystal imbedded in negative permittivity material. Two experimental realizations are proposed that it is possible to build up a demonstration platform working at microwave frequencies to verify corresponding topology physics theories using simple photonic crystal structures. We hope that the successful verification of new topology physics can further trigger applications in optics.