This paper presents a discrete-time multi-stage noise shaping (MASH) delta-sigma modulator (DSM) with second-order digital noise coupling for wideband high-resolution applications. By directly injecting the output of the second loop into the quantizer input of the first loop while choosing an appropriate signal transfer function of the second loop, a second-order digital noise coupling can be easily constructed without almost imposing any hardware complexity. With the help of the second-order digital noise coupling, the inherent quantization noise leakage in the MASH topology is significantly mitigated, thus resulting in less DC gain requirement for the integrators. Mathematical analysis and further simulation results are presented to demonstrate the effectiveness of the proposed MASH structure.