The moment stability of a damped Mathieu oscillator to combined deterministic harmonic and random noise of the form of a stationary Gaussian process parametric excitation is investigated. The analysis is based on a suitable coordinate transformation and stochastic averaging method

which reduces the system to two linear Ito's stochastic differential equations. By using the Ito's differential rule

differential equations ruling the time evolution of the first and second order response moments are 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 is obtained

while results of the second order moment stability are given numerically. Some numerical simulations and graphs are presented for representative cases. It is founded that，when the intensity of the random noise and the amplitude of the deterministic harmonic excitation increase

the stability regions will reduce whether for the first order moment or the second order moment stability. The stability regions will reduce to the minimum value if the detuning parameter tend to zero. The stability regions based on different order moments will become identical when the intensity of the random noise increases to zero.