In this paper, we propose a discrete-time host-pathogen model and study its qualitative behavior. The model is for the spread of an infectious disease with constant mortality rate of hosts. Moreover, the time-step is equal to the duration of the infectious phase and the host mortality is taken at some constant rate d >0. This two-dimensional discrete-time epidemic model has complex dynamical behavior. More precisely, we investigate the existence and uniqueness of positive equilibrium point, boundedness character, local and global asymptotic stability of unique positive equilibrium point, and the rate of convergence of positive solutions that converge to unique positive equilibrium point. Numerical simulations are provided to illustrate our theoretical results.