A free-form (FF) surface design method is proposed for a nonaxial-symmetrical projector system comprising an FF reflector and a light source. The profile of the reflector is designed using a nonaxial-symmetrical FF (NFF) surface construction method such that each incident ray is directed in such a way as to form a user-specified image pattern on the target region of the image plane. The light ray paths within the projection system are analyzed using an exact analytical model and a skew-ray tracing approach. The validity of the proposed NFF design method is demonstrated by means of ZEMAX simulations. It is shown that the image pattern formed on the target region of the image plane is in good agreement with that specified by the user. The NFF method is mathematically straightforward and easily implemented in computer code. As such, it provides a useful tool for the design and analysis stages of optical systems design.