Abstract: A statistical linearization method for calculating the second-order moment of a non-linear oscillator endowed with fractional derivative damping under combined random and harmonic excitations is proposed. Assuming the system response to be written as the sum of a deterministic mean component and a zero-mean random component，the motion differential equation can be separated into two coupled differential equations of the deterministic and random parts. The method of harmonic balance and the method of statistical linearization are used to solve the two differential equations respectively to access the deterministic and random components of the response. The effectiveness of the method is verified by Monte Carlo simulation.