To speed up the acquisition time of multi-dimensional magnetic resonance spectroscopy (MRS), one typical way is to sparsely acquire free induction decay (FID) data reconstruct the spectrum from the incomplete observations. Recently, a low rank Hankel matrix (LRHM) approach, that explores the sparse number of spectral peaks, has shown great ability to reconstruct the spectrum. When the data are highly undersampled, however, low intensity spectral peaks are compromised in the reconstruction. In this abstract, a weighted LRHM approach is proposed. A weighted nuclear norm is introduced to better approximate the rank constraint, and a prior signal space is estimated from the pre-reconstruction to reduce the number of unknowns in reconstruction. Results on both synthetic and real MRS data demonstrate that the proposed approach can reconstruct low intensity spectral peaks better than the state-of-the-art LRHM method.