Antibiotic resistance is a significant public health problem. When resistance genes are being carried on plasmids, the spread can be greatly accelerated. In this paper, the transmission of antibiotic resistance in two types of cells is discussed. A mathematical model is established to describe the dynamics of the transmission of plasmids. The effects of different parameters on the stable solution and sensitivity analysis are studied by numerical simulation. The conclusions show that the concentration of antibiotics must reach a certain level to kill the pathogenic bacteria. If the concentration of antibiotics is not high to a certain extent, the treatment becomes ineffective. If the cost of cells carried on plasmids and the rate of resistance plasmids segregation too high, the drug-resistant cells will gradually die out in the system. The rate of horizontal transfer of resistance plasmids is directly related to the spread of drug resistance. With the increase in the horizontal transfer rate of resistance plasmids, cells in the body gradually turn into cells with antibiotic resistance, which causes substantial difficulties in the treatment of diseases.