A dynamic analysis of the passive constrained layer damping (PCLD) beam considering randomness of viscoelastic damping layer was studied by using the transfer function method. With an introduction of the state vector, the governing equation of the PCLD beam in state space was established from the six-order differential motion equation，which was derived by using the Hamilton principle. The closed-form solutions of natural frequencies and loss factors of a PCLD beam were obtained by the distributed parameter transfer function method. The parameters in fractional derivative model of viscoelastic material were regarded as the base random variables, which follow normal distribution in this analysis. The influence of parameter randomness on the natural frequency and the mode loss factor of the structure were analyzed by using the Monte Carlo method. Numerical examples show that the randomness has obvious effects on the correlation coefficient of dynamic characteristic, and the maximal value of the loss factor's correlation coefficient is about 4.5 times as much as the one of material parameter. So it is necessary to carry out the random analysis for PCLD structures.