Image registration is a prerequisite for image fusion from multiple modalities, such as infrared (IR) and visible (VIS) images. Although there have been many various methods of image registration, non-rigid registration for IR and VIS images is still challenging due to large differences between IR and VIS images. In this work, a point feature-based method is proposed to improve the performance on non-rigid IR and VIS image registration. Firstly, a feature descriptor -Gaussian weighted shape context (GWSC) -is improved from shape context (SC) to fast extract matching point pairs from edge maps in IR and VIS images. With the set of matching point pairs, a Gaussian-field-based objective function is established to measure the distance between IR and VIS images. Then, the enhanced affine transformation (EAT) model is proposed to generalize affine model from linear to non-linear case and describe the regularity of global deformation between IR and VIS images. At last, the derivative of the distance measure is expressed with respect to the EAT model and thus, the optimal parameters are estimated by using the quasi-Newton method. The qualitative and quantitative comparisons demonstrate that the proposed method (GWSC-EAT) can be successfully applied to non-rigid registration of IR and VIS images and moreover, it is superior to the state-of-the-art methods on the accuracy and speed of non-rigid registration.