Since local feature descriptors extracted from an image using the traditional scale-invariant feature transform (SIFT) method are 128-dimensional vectors, the matching time is too long, which limits their applicability in some cases such as feature point matching based on the three-dimensional reconstruction. To tackle this problem, a SIFT feature descriptor dimensionality reduction method based on a convolutional neural network is proposed. The powerful learning ability of the convolutional neural network is used to realize the dimensionality reduction of SIFT feature descriptors while maintaining their good affine transformation invariance. The experimental results demonstrate that the new feature descriptors obtained using the proposed method generalize well against affine transformations, such as rotation, scale, viewpoint, and illumination, after reducing their dimensionality to 32. Furthermore, the matching speed of the feature descriptors obtained using the proposed method is nearly five times faster than that of the SIFT feature descriptors.