An off-axis optical system with an x-y polynomial surface for a see-through head-mounted display (HMD) is presented. With the use of an x-y polynomial surface, an off-axis see-through HMD system with one tilted spherical combiner and six relay optical lenses is designed. An off-axis see-through HMD with a 15 mm exit pupil, a 40 degrees x 30 degrees FOV, and 70 mm eye relief is achieved. Furthermore, a binocular off-axis see-through HMD prototype is fabricated and the performance of the system is experimentally tested; 972 cd/m(2) of luminance is measured at the position of the exit pupil of the HMD. A typical augmented reality image captured outdoors with the HMD prototype is also demonstrated.