The BIFROST instrument will be the first VLTI instrument optimised for high spectral resolution up to R=25,000 and operate between 1.05 and 1.7 μm. A key component of the instrument will be the spectrograph, where we require a high throughput over a broad bandwidth. In this contribution, we discuss the four planned spectral modes (R=50, R=1000, R=5000, and R=25,000), the key spectral windows that we need to cover, and the technology choices that we have considered. We present our plan to use Volume Phase Holographic Gratings (VPHGs) to achieve a high efficiency > 85%. We present our preliminary optical design and our strategies for wavelength calibration.