Nonrigid image registration plays an important role in the field of computer vision and medical application. The methods based on Demons algorithm for image registration usually use intensity difference as similarity criteria. However, intensity based methods can not preserve image texture details well and are limited by local minima. In order to solve these problems, we propose a Gabor feature based LogDemons registration method in this paper, called GFDemons. We extract Gabor features of the registered images to construct feature similarity metric since Gabor filters are suitable to extract image texture information. Furthermore, because of the weak gradients in some image regions, the update fields are too small to transform the moving image to the fixed image correctly. In order to compensate this deficiency, we propose an inertial constraint strategy based on GFDemons, named IGFDemons, using the previous update fields to provide guided information for the current update field. The inertial constraint strategy can further improve the performance of the proposed method in terms of accuracy and convergence. We conduct experiments on three different types of images and the results demonstrate that the proposed methods achieve better performance than some popular methods.