In this paper, we present the design, optimization, and implementation of a sub-wavelength grating (SWG) multi-mode interference coupler (MMI) on the silicon nitride photonic integrated circuit (PIC) platform with a significantly enhanced bandwidth compared to the conventional MMI. We extend the SWG MMI theory, previously presented for the silicon-on-insulator platform, to the Si3N4/SiO2 platform. Our approach involves an initial parameter optimization for a non-paired design, followed by a shift to a paired design that offers a smaller footprint and a broader bandwidth. The optimized SWG MMI exhibits a 1 dB bandwidth of 300 nm for both the insertion loss and power imbalance, making it a significant addition to silicon nitride photonics.