Infrared detectors are being developed for high resolution and small pixels. To detect small pixels, an infrared optical system must have a small F-number. Therefore, based on the demand for small-pixel detection, this study designed an off-axis three-reflection infrared optical system with an F-number close to 1 using a Cook-type off-axis three-reflection structure. The primary, secondary, and tertiary mirrors of this optical system were all aspherical, with an F-number of 1.3, focal length of 60 mm, field of view of 1.6°×2.4°, and a wavelength band of 1.1–2.5 μm. The modulation transfer function (MTF) of this infrared optical system design was greater than 0.6 at a spatial cutoff frequency of 100 line pairs per millimeter. The RMS value of the diffuse spot was smaller than the pixel size of the detector, with a distortion of less than 2%. The system design and simulation results indicated that the MTF of each field of view was close to the diffraction limit, meeting both imaging quality and small-pixel detection requirements.