Abstract: Compressed Sensing (CS) reconstruction of hyperspectral image is an effective mechanism to comedy the traditional hyperspectral imaging pattern with the drawback of high redundancy and vast data volume. This paper presents a new multiple measurement vector model for compressed sensing reconstruction of hyperspectral data in consideration of its multiple channel character. In the encoding side, the random convolution operator is used to rapidly obtain the measurement vector of each channel which is subsequently reorganized as a measurement vector matrix. In the decoding side, a joint reconstruction model is proposed to reconstruct the hyperspectral data from the multiple measurement vectors. The model decomposes the hyperspectral data into the inter-channel correlated and differenced component in the sparsifying transform domain, where the correlated component with high spatial and spectral correlation is constrained to be graph structured sparse and the differenced component is constrained to be sparse. A numerical optimization algorithm is also proposed to solve the reconstruction model by the alternating direction method of multiplier. Every sub-problem in the iteration formula admits analysis solution by introducing the auxiliary variable and linearization operation. The complexity of the numerical optimization algorithm is reduced. The experimental results demonstrate the effectiveness of the proposed algorithm.