Abstract: We propose a Bayesian smoothness prior in the spectral fitting of MRS images which can be used in addition to commonly employed prior knowledge. By combining a frequency-domain model for the free induction decay with a Gaussian Markov random field prior, a new optimization objective is derived that encourages smooth parameter maps. Using a particular parameterization of the prior, smooth damping, frequency and phase maps can be obtained whilst preserving sharp spatial features in the amplitude map. A Monte Carlo study based on two sets of simulated data demonstrates that the variance of the estimated parameter maps can be reduced considerably, even below the Cramér-Rao lower bound, when using spatial prior knowledge. Long-TE 1H MRSI at 1.5 T of a patient with a brain tumor shows that the use of the spatial prior resolves the overlapping peaks of choline and creatine when a single voxel method fails to do so. Improved and detailed metabolic maps can be derived from high-spatial-resolution, short-TE 1H MRSI at 3 T. Finally, the evaluation of four series of long-TE brain MRSI data with various signal-to-noise ratios shows the general benefit of the proposed approach.