This paper presents a new multi-stage noise-shaping (MASH) digital delta-sigma modulator (DDSM), denoted as HJ-MASH DDSM which can remove spurs in the output spectrum and has long sequence lengths than Jinook structure and HK-MASH in the worst input case by applying HK-EFM in the first stage error feedback modulator (EFM) of the DDSM. In addition, the proposed HJ-MASH DDSM lowers the difficulty of constructing higher order MASH DDSMs compared to HK-MASH DDSM. While the performance and stability are all superior to Jinook structure for all constant inputs, especially for the input which correspond to minimum cycle lengths. The digital delta-sigma modulator applied in fractional-N frequency synthesizers ameliorates the synthesizer’s spectral purity apparently by verification.