Magnetic resonance spectroscopy (MRS) is commonly converted from its free induction decay (FID) data with Fourier transform. How to reconstruct high quality spectra is one of the fundamental problems for MRS. In this work, a reconstruction method is proposed to explore the general exponential property of FID. Each exponential function of FID is explicitly enforced with the Hankel matrix Vandermonde Factorization (HVaF). This model is then applied to spectrum reconstruction of sparsely sampled FID in fast MRS. Results on synthetic and realistic MRS show that the new approach requires fewer data to allow successful reconstruction and provides better reconstruction on low-intensity signals than the state-of-the-art low rank Hankel matrix method. Thus, the new approach would be useful for faster data acquisition or recovery of weak spectral peaks in MRS applications.