Within the time-nonlocal quantum master equation description, we develop an efficient method for calculating the noise spectrum of transport current through interacting mesoscopic systems. By introducing proper current-related density operators, we propose a practical and very efficient time-local equation of motion implementation to compute the noise spectrum, which contains the full information of emission and absorption. We obtain an analytical expression to characterize the nonequilibrium transport including Coulomb interaction and memory effect. We demonstrate the proposed method with double quantum dots systems and find good agreement with the exact results, whenever the system-reservoir coupling is smaller than the temperature.