Wedge filter spectral imager, with no moving components and low complexity, has become an important development direction of low cost miniature imaging spectrometer. Based on the state of the art hyperspectral lossless compression standard CCSDS123, we propose a lossless data compression method for the wedge filter spectral imager. The proposed method redefines the local difference vector in CCSDS123, taking fully advantage of the spatial-spectral co-modulation characteristics of the wedge filter spectral imager. To compress the raw data from a wedge filter spectral imager, the compression encoder firstly predicts the sample value using its local sum and local difference vector, then computes a prediction residual and the corresponding mapped prediction residual, finally encodes the mapped prediction residual via a sample-adaptive entropy coding approach. The proposed method can effectively compress the raw data from a wedge filter spectral imager by using the local correlation in the spatial-spectral space. To verify the compression performance of the proposed method, experiments are taken on 6 raw datasets containing different scenes. The results show that the proposed method surpasses the original CCSDS123 method by about 21.62% higher compression ratio on the test datasets with almost the same computational time.