In the scale-invariant feature transform (SIFT) algorithm, directional stability is a significant factor which affects the matching results between key points. This paper proposes adaptive kernel regression function as a replacement for the original Gaussian function in order to weigh the gradient direction around the key points for image registration. The gradient information is included in the weighting function. For changes in flat areas, the weight function is shaped as a circle-like function while in edged areas it is shaped as ellipsoid-like function. More stability between key points is achieved with the adaptive weight function. More stabile direction of key point is got. Some experimental results on standard test set of image registration show the feasibility of this method.