An image mapping spectrometer (IMS) is a kind of snapshot imaging spectrometer characterized by containing several array components including the image mapper, prism array, and reimaging lens array. We propose a hybrid non-sequential modeling method of IMS and present the complete optical model of the system built in Zemax. This method utilizes the spatial periodicity of the array components and requires only a small number of input parameters. Moreover, we design a collimating lens of a large relative aperture, sufficient working distance, and low aberration to meet the requirements of an IMS with good optical performance and compact volume. The designed lens is quantitatively evaluated in the entire IMS model, and the results demonstrate that the lens has excellent optical performance. The evaluation on the collimating lens also demonstrates the capability of the proposed modeling method in the design and optimization of systems such as the IMS that contain multiple array components. The designed collimating lens is manufactured and assembled in the experimental setup of the IMS. The proposed modeling method is verified by experimental results.