The principle and instrumental structure of dispersion Hadamard transform spectral imager were briefly described in the present paper, and the disadvantages of the imager both in dislocation of spatial and spectral information and in spectral resolution limited by the width of Hadamard encoding mask were pointed out. A new instrumental principle and design of spatially modulated interference Hadamard transform spectral imager was proposed. A lateral shearing interferometer was used to acquire interference signals of all the Hadamard encoding information at different optical path difference. Then the methods of Fourier transform and Hadamard transform for interferogram were performed to acquire the spectra of objectives. Theory analysis of this imager demonstrated that the modulation of interferogram would not be affected by some factors such as the form and size of Hadamard encoding mask, and the spectral resolution would not be influenced by the size of Hadamard encoding mask. Furthermore, such technique not only effectively eradicated the dislocation of spatial information and spectral information existing in dispersion Hadamard transform spectral imager, but also made it convenient to image with high-throughput, high spatial resolution and high spectral resolution.