In this work, the random vibration characteristics of a beaded rope under a concentrated load are investigated. A stochastic model describing the sawing force of a single diamond-beaded rope was established, based on the principle of volume invariability. The governing equations of the beaded rope were obtained using Hamilton's principle. Theoretical expressions were derived to calculate the response power spectral density (PSD), load-response cross-PSD and the mean square value of the beaded rope lateral displacement, for a beaded rope subject to a concentrated load. The influence of the parameters on the random vibration characteristics of a beaded rope was analyzed, including the effects of the linear speed of the beaded rope, the tension of the beaded rope, and the location of the concentrated load. Numerical examples are given. Results show that as the tension of the beaded rope increases, the PSD and mean square value of the rope displacement are reduced. However, as the linear velocity of the beaded rope increases, the PSD and mean square value of the rope displacement are also increased. During movement of the diamond-beaded rope, the mean square value of the transverse displacement fluctuates predominantly, because of the time-varying impact force caused by the diamond beads.