A new method to retrieve sea surface wind direction using synthetic aperture radar image is presented. Some pretreatment steps such as suppressing noise, down sampling and dividing into several sub-images are presented first. The method of two-dimensional numerical differentiation based on Tikhonov regularization is introduced to compute the gradient direction in the sub-image intensity of every point. The distance weighted objective function is used to compute the overall gradient direction in the sub-images. The retrieved wind direction is orthogonal to the overall gradient. When adding 10% of random errors, numerical simulations show that the result of numerical differentiation is better than that from the Sobel operator which is based on the finite difference method: the former error is 0.7293 , and the latter error is 13.5069 . Finally, an experiment based on real SAR data shows that the wind direction deviates from the overall direction determined by the method of Sobel operator, and the direction determined by the method of numerical differentiation is consistent well with the overall wind direction. Comparing the ship board wind direction and the corresponding location wind direction retrieved from the synthetic aperture radar sub-images with the two methods, the average result error of Sobel operator method is 9.0331, while that of numerical differentiation method is 1.1148. This new method is an effective and high accurate method to retrieve the sea surface wind direction of synthetic aperture radar image.