Coupled slow waves, slow acoustic waves, and electromagnetic waves are simultaneously achieved based on a piezoelectric material, in which a line defect is created within a honeycomb lattice array of cylindrical holes etched in a LiNbO_3 slab. Finite element simulations in frequency domain and time domain demonstrate that a highly localized slow mode is obtained in the defect. Owing to the piezoelectricity of LiNbO_3, acoustic and electromagnetic waves are coupled with each other and transmit along the line defect. Therefore, in addition to a slow acoustic wave, an electromagnetic wave with a group velocity even lower than conventional acoustic waves is achieved. Coupled slow waves, slow acoustic waves, and electromagnetic waves are also based on a piezoelectric material, in which a line defect is created within a honeycomb lattice array of cylindrical holes etched in a LiNbO_3 slab. Finite element simulations in frequency domain and time domain demonstrate that a highly localized slow mode is obtained in the defect. Owing to the piezoelectricity of LiNbO_3, acoustic and electromagnetic waves are coupled with each other and transmit along the line defect. a group velocity even lower than conventional acoustic waves is achieved.