the off-axis parabolic collimator with eccentric pupil has the advantages of wide spectrum, simple structure, easy assembly and adjustment, high performance price ratio.so, it is widely used for parameters testing and image quality calibration of ground-based and space-based cameras. in addition to the strehl ratio, resolution, wavefront aberration, modulation transfer function, the general evaluation criteria on the imaging quality of the optical system, the beam parallelism characterize the collimator angle resolving capability and collimation condition of the collimator with the target board, can be measured easily, quickly and operation process is simple, but the study mainly focus on how to measure it so far.in order to solve quantitative calculation of this problem, firstly, the discussion of aberration condition of the off-axis parabolic is carried out based on the the primary aberration theory. secondly, analysis on the influencing factor on collimator optical properties is given, including the geometrical aberrations of spherical aberration, coma, astigmatism, the relation between the position of the eccentric pupil and the aberration and optical element surface wavefront aberration, after that, according to the basis of diffraction and wavefront aberration theory, the paper deduced calculation method of the beam parallelism, at last, an example of a 400mm diameter off-axis parabolic collimator with eccentric pupil is given to caculate, the practical results shows that calculation data is well in accordance with actual measurement data and results can meet the demand and has a guiding significance to the actual project manufacture and the theory analysis. © 2017 spie.