  We present an analytical study of the mode degeneracy in non-Hermitian
photonic crystals (PC) with $C_{4v}$ symmetry, from the perspective of the
coupled-wave-theory (CWT). The wave couplings and leakages within the
non-Hermitian PCs are depicted, and the condition of accidental triple
degeneracy is derived which leads to a Dirac-cone like dispersion. We prove
that, similar to the real Dirac-cone, the Dirac-cone like band in non-Hermitian
PC possesses good linearity and isotropy in the vicinity of the $\Gamma$ point.
Moreover, some topological transit of the band may occur when the parameters
adiabatically evolve. However, the Berry phase remains zero at the $\Gamma$
point, indicated the Dirac-like-cone dosen't obey Dirac equation and it is only
Dirac-cone.
