On the basis of the imaging model of an interferometric imaging spectrometer, a novel model with a priori constraints is proposed to recover spatial and spectral information simultaneously. The nonnegative low rank property and total variation (TV) regularization are adopted to constrain the strong spectral correlation and spatial piecewise smoothness of recovered hyperspectral image, respectively. Meanwhile, the sparse noise and Gaussian noise in interferometric data are modeled by the L₁ norm and Frobenius norm, respectively. The effectiveness of the proposed method is verified through comparative experiments on simulated and real interferometric data. Compared with traditional recovery methods for interferometric data, the proposed method not only recovers the spectral information of the object accurately but also effectively eliminates the degradation effect of mixed noise in the interferogram. As a result, the data quality of the recovered hyperspectral image is improved.