This study evaluates the response reduction effect of single-degree-of-freedom (SDOF) primary systems with multiple tuned mass dampers (MTMDs) under harmonic excitation. To design MTMD, TMD properties are re-calibrated based on the natural frequencies of the system on which the number of TMDs is one less than the current system. This is a sequential approach that does not require any iteration for each step. Instead it requires starting from the case with single TMD, and then increasing the numbers of TMDs one more at a time until the desired number is reached. Using the obtained design parameters, the effectiveness and robustness of the MTMDs are studied in comparison to MTMDs designed by previous works available in the literature. As a result, the proposed design procedure produces an effective multiple tuned mass damper to be utilized in a SDOF system under harmonic excitation. Additionally, the proposed approach provides a simple way to design the MTMD system than the traditional optimization methods, thus it significantly reduces the computation effort in the design process.