IR optical systems such as Petzval doublet refractive lenses or Cassegrain reflective mirrors are either expensive or poor in image quality. Taking advantage of the low cost of reflective mirrors, here we present an optical design of Double Cassegrain reflective mirrors consisting of two sets of Cassegrain reflectors facing each other symmetrically. This symmetry also cancels many aberrations besides the chromatic aberration-free nature of reflective mirrors. Design results show that this system is better than Cassegrain reflectors in aberration correction and image resolution, but cheaper than Petzval doublet refractive lenses systems in price. IR cameras with this optical system could be widely used for body temperature measurement and security check.