The ray-tracing method is applied to get the numerical model of the system, and then a series expansion method is used to establish a three-order analytical model. The analytical model provides analytical expressions of aberration coefficients and spot diagrams, adapts to the system containing a varied line spacing convex grating, and has strong scalability. The complete imaging performance can be quickly evaluated by the analytical expressions of spot diagrams. By tracking 10000 rays with different wavelengths and heights in an Offner example system, the results show that analytical model can quickly reproduce the spot diagrams with a high degree of accuracy. With these formulas coma, spherical aberration, astigmatism and distortion are discussed in detail. The analytical model provides theoretical guidance for the optimal design of Offner imaging spectrometers.