In this paper, the propagation of electromagnetic waves in a periodic structure is described by the coupled-wave equations. We find the coupled-wave equations for the waveguides containing LHM cover, and the coupling between two forward and backward modes in LHM waveguides grating is discussed. The transverse and longitude coupling coefficients for the TE modes is obtained and is more complex than the results for RHM waveguide gratings. Also our results show considerable enhancement in the coupling coefficient for triangular structure. On the other hand, longitude coupling coefficient isn’t zero.