In this paper we propose an efficient sparse reconstruction scheme for the parallel MRSI data acquired using a fast spiral scheme. We model the system using the MR priors estimated from the water reference scan. In our sparse reconstruction approach, we minimize the total variation and norm of the compartmentalized MRSI data in order to reduce noise, inhomogeneity distortions, and spectral leakage. We demonstrate significant improvement for in vivo brain results when compared to classical regularized SENSE MRSI reconstruction.