A new method to solve the zoom equation is presented. For the middle infrared 320×256 element cooled thermal focal plane array detector, an optical system of 3.7～4.8 μm refractive infrared continuous zoom is designed, which has a constant F number of 2, a minimum focal length of 22 mm, and a zoom ratio of 6. This system is composed of a zoom objective and a secondary imaging system, including 7 lenses made of silicon or germanium in total. In order to correct off-axis aberrations, aspherical surfaces are used. Meanwhile, two folding mirrors are introduced to reduce the volume of this system. The modulation transfer function of each field of view is above 0.55 in all focal positions at the spatial frequency of 16 lp/mm. The energy permeance ratio is greater than 80% within the inscribed circle limited by the detector sensor with the size of 30 μm×30 μm. So the continuous zoom system has a good imaging quality.