A medium infrared optical system was designed for acoustooptic tunable filter spectra camera to obtain the spatial information and spectral information.By introducing a hybrid refractive/diffractive lens,there are six lens in the fore zoom optical system to achieve 12× zoom ratio,which can identify the object 2 000 m far at long focal length.ZEMAX software was used to simulate the diffraction of the crystal,a wedge with 4° is needed to certify that the -1 order diffraction beams exit coaxially.Results show that the maximum modulation transfer function at spatial frequency14 lp/mm of the whole system is 0.7,the diffraction encircled energy was greater than 90%,which satisfy the image quality of the spectrum camera for target identifying and tracking.