A technique coupling with the parameter transformation method and the multiple scales method is presented for determining the primary resonance response of strongly non-linear Duffing-Rayleigh oscillator to random narrow-band excitation. By introducing of a new expansion parameter, the multiple scales method is employed to determine the equations describing the modulation of the amplitude and phase. The dynamical behaviors of the primary resonance response are analyzed in detail. The effect of the random excitation on the stable periodic response is analyzed as a perturbation and stationary mean-square response is obtained by the moment method. Sufficient and necessary condition for stability of the steady-state response is obtained by Routh–Hurwitz criterion. Theoretical analyses in addition to numerical calculation show that under some conditions the system may have two steady-state solutions. Theoretical results are verified by numerical ones and good agreement is found. The results obtained for strongly non-linear oscillator complement previous results in the literature for weakly non-linear oscillator.