A light field modulated imaging spectrometer (LFMIS) can acquire the spatial-spectral datacube of targets of interest or a scene in a single shot. The spectral information of a point target is imaged on the pixels covered by a microlens. The pixels receive spectral information from different spectral filters to the diffraction and misalignments of the optical components. In this paper, we present a linear spectral multiplexing model of the acquired target spectrum. A calibration method is proposed for calibrating the center wavelengths and bandwidths of channels of an LFMIS system based on the liner-variable filter (LVF) and for determining the spectral multiplexing matrix. In order to improve the accuracy of the restored spectral data, we introduce a reconstruction algorithm based on the total least square (TLS) approach. Simulation and experimental results confirm the performance of the spectrum reconstruction algorithm and validate the feasibility of the proposed calibrating scheme.