To avoid the problems of the classical interference imaging spectrometer, such as poor stabilization, and intractable interference fringes, a novel polarization interference imaging spectrometer based on a new adjustable lateral displacement Savart polariscope is developed. The effect of the incident angle on the optical path difference, state of polarization and interference fringes of the system is deduced in detail. The work principle and operation mode of this spectrometer are also analyzed, which proves that this interference imaging spectrometer has less weight, smaller capacity, better vibrational resistance, splitted beams with parallel and uniform distribution, and clear interference pattern, and can be widely used in many different fields. The theoretical and practical guidance is thereby provided for the study, design, and debugging or engineering of the new polarization interference imaging spectrometers with adjustable lateral displacement.