Abstract: The stochastic resonance (SR) in the memorial under-damped system with time delay feedback and fluctuating mass is investigated in this paper. The non-Markovian original system is reformulated into two-dimensional Markovian linear system through introducing variable transformations and using the small time delay approximation. Further, the analytic expressions for the first moment of the response and the steady response amplitude are derived by using the Shapiro-Loginov formula and the Laplace transformation technique. All the research results show that when the Routh-Hurwitz stability is satisfied, the phenomenon of SR is shown with the variations of mass fluctuation noise intensity, driving frequency and time delay, respectively. The stochastic multi-resonance phenomenon is also observed. Moreover, the SR is enhanced with an increase in time delay by introducing the time delay feedback and instead, the SR is suppressed for large memory time and damping parameter. By adjusting the time delay feedback and the memory effects, the response of the system to a harmonic signal can be further improved. Finally, the theoretical results are well verified through numerical simulations