As a global feature of the fingerprint, the orientation field is very important to an automatic fingerprint identification system (AFIS). Establishing an accurate and precise model for the orientation field will not only improve the performance of orientation estimation, but will also make it feasible to apply orientation information into the matching process. Such a novel model for the orientation field for a fingerprint is proposed. We use a polynomial model to approximate the orientation field globally and a point-charge model at each singular point to improve the approximation locally. These two models are combined together by a weight function. Experimental results are provided to illustrate that this combination model is more accurate and robust to noise compared with previous works. Its applications are also discussed.