An SIS epidemic model with mutating pathogens is investigated. The constant recruitment rate and exponential natural death, as well as the disease-related death, are incorporated into the model. The basic reproduction numbers of two strains are found. The global stability of the disease-free equilibrium is obtained, the global stability of the boundary equilibrium (infection of Strain 2) and coexistent equilibrium of two strains is gotten under the case that the infection is not fatal.