In this report an infrared zoom optical system is discussed. This system shifts a single moving element to switch between two focal lengths(30mm/60mm), one for wide angle and the other for close-up. However, a conventional optics-only method cannot provide good imaging quality over a large depth of focus at each focus offset. To improve the imaging performance, we investigate a lens-combined modulated wavefront coding technology for extending the depth of focus. Instead of placing a phase mask at the pupil position like traditional wavefront coding does, all the element surfaces in the system contribute to achieving modulation transfer function (MTF) consistency over a large range of depth of focus under dual field-of-view settings. As a result, the new structure extends the depth of focus 6.5 times than that of the original system. We also demonstrate recovered images employing hyper-Laplacian priors with noise and artifacts suppressed. It is concluded that the novel structure can not only extend the depth of focus but also reduce the complexity of infrared optical system.