We investigate the existence and multiplicity of positive steady-state solutions to the unstirred Chemostat model with Beddington-DeAngelis functional response. The global structure of coexistence solutions is studied by the bifurcation theory. Sufficiently conditions for the existence of positive steady-state solutions are obtained. Furthermore, the stability and multiplicity of positive steady-state solutions are discussed. Conditions for the multiple existence of positive steady-state solutions are established by means of the perturbation theory for linear operators and the fixed point index theory. The results indicate that the maximal growth rate of the plasmid-bearing organism has an effect on the stability and multiplicity of positive steady-state solutions.