We study edge modes in topological semi-metals which have an energy band structure of ordinary semi-metals but can be characterized by a Chern number. More specifically, we focus on a Qi-Wu-Zhang-type square-lattice model and a Haldane-type honeycomb model, both of which exhibit anti-chiral edge modes whose wave packets propagate in the same direction at both parallel edges of the strip. In order to obtain these analytical solutions of the edge modes, we apply the transfer matrix method which was developed in the previous work [Phys. Rev. B \textbf{101}, 014442 (2020)]. As a result, we show that the bulk-edge correspondence is broken down for a certain range of the model parameters. More precisely, when increasing the strength of a hopping amplitude of the models, the edge modes abruptly disappear, although the non-trivial Chern number does not change.