A freeform optical system of automotive Head-Up Display (HUD) was designed. In the initial layout design of the HUD optical system, the sample points on two optical freeform surfaces of the HUD optical system are calculated by the seed curve extension algorithm. And the two freeform surfaces are expressed by the extended polynomials. Then the ray tracing is performed for the initial layout of the HUD optical system at center field of view with 0.5 mm ray sampling interval. The results show that the performance of the initial layout of the HUD optical system is the diffraction-limited, which can be used as the starting point for further optimization at full field of view. After optimization, the final HUD optical system is obtained. In order to simulate the observation of human eyes, several test points in the Eyebox are taken as object points, which are imaged on the image plane by the HUD optical system. The modulation transfer function plots of the several test points are greater than 0.5 at 6 lp/mm, which are close to diffraction limit. And the distortions of the final HUD system are less than 2%. Finally, the manufacture tolerances of two optical freeform surfaces are analyzed. The results show that the modulation transfer function plots of the HUD optical system are higher than 0.3 with the tolerance PV values of 0.42 μm and 0.62 μm of the two optical freeform surfaces respectively. For the current machining capacity, the tolerance requirements are reasonable.