This work presents a new approach for high-resolution MRSI of the brain at 7 T in clinically feasible measurement times. Two major problems of MRSI are the long scan times for large matrix sizes and the possible spectral contamination by the transcranial lipid signal. We propose a combination of free induction decay (FID)-MRSI with a short acquisition delay and acceleration via in-plane two-dimensional generalised autocalibrating partially parallel acquisition (2D-GRAPPA) with adiabatic double inversion recovery (IR)-based lipid suppression to allow robust high-resolution MRSI. We performed Bloch simulations to evaluate the magnetisation pathways of lipids and metabolites, and compared the results with phantom measurements. Acceleration factors in the range 2–25 were tested in a phantom. Five volunteers were scanned to verify the value of our MRSI method in vivo. GRAPPA artefacts that cause fold-in of transcranial lipids were suppressed via double IR, with a non-selective symmetric frequency sweep. The use of long, low-power inversion pulses (100 ms) reduced specific absorption rate requirements. The symmetric frequency sweep over both pulses provided good lipid suppression (>90%), in addition to a reduced loss in metabolite signal-to-noise ratio (SNR), compared with conventional IR suppression (52–70%). The metabolic mapping over the whole brain slice was not limited to a rectangular region of interest. 2D-GRAPPA provided acceleration up to a factor of nine for in vivo FID-MRSI without a substantial increase in g-factors (<1.1). A 64 × 64 matrix can be acquired with a common repetition time of ~1.3 s in only 8 min without lipid artefacts caused by acceleration. Overall, we present a fast and robust MRSI method, using combined double IR fat suppression and 2D-GRAPPA acceleration, which may be used in (pre)clinical studies of the brain at 7 T. © 2015 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.