The random response of dielectric elastomer balloon subjected to random pressure and constant voltage is investigated, where the mechanical property is described by Gent model in order to consider the strainstiffening effect of the dielectric elastomer, and the random pressure is described by Gaussian white noise. By introducing the energydependent transformation and using the stochastic averaging, the reduced FokkerPlanckKolmogorov equation governing the stationary probability density of the system total energy is derived, which can be analytically solved. The marginal probability densities of the stretch ratio and its change ratio are then calculated, as well as the mean value and the meansquare value of the stretch ratio. Two typical cases are investigated in detail, i.e., one is with the stretch ratio of balloon vibrating of around 1 and the other is that around the extension limit. The influences of the random excitation intensity, material parameter and the constant voltage on the statistics of the stretch ratio are discussed in detail. Different values of the material parameter and the constant voltage can cause completely different random vibration behaviors. The efficacy and accuracy of the proposed procedure are eventually verified by comparing with the results from Monte Carlo simulation.