This paper investigated the resonance response and moment stability of a single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to boundary random parametric excitation. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the applications of asymptotic averaging over the period for slowly varying random process. By using the It?'s differential rule, the differential equations ruling the time evolution of the first and second order response moments were obtained. The necessary and sufficient conditions of stability for the first and second order moments are that the matrix of the coefficients of the differential equations ruling the moments have complex eigenvalues with negative real parts. The analytical expression of the stability condition of the first order moment was obtained, while the results of the second order moment stability were given numerically. Some numerical simulations and graphs were presented for representative cases. It is founded that, when the amplitude of the parametric excitation increases, the stability regions will reduce either for the first order moment or the second order moment stability. The stability regions will reduce to the minimum value if the detuning parameter tends to zero. The stability regions based on different order moments will become identical when the intensity of the random disturbance increases to zero. In some cases the stochastic excitation stabilizes the system.