This paper aims to investigate the response of single-degree-of-freedom (SDOF) system with Caputo-type fractional derivative damping term under Gaussian white noise excitation.First, the approximately analytical solution of the system is obtained by using the stochastic averaging method.Then, an effective algorithm for the solution of initial value problems with Caputo derivative is briefly introduced.At last, in order to certify the validity of the analytical solution, two examples are worked out in detail.A very satisfactory agreement is found between the analytical results and the Monte Carlo simulation of original systems.