Multi-source image registration often suffered from great radiation and geometric differences. Specifically, gray scale and texture from similar landforms in different source images often show significantly different visual features. And these differences disturb the corresponding point extraction in the following image registration process. Considering that edges between heterogeneous images can provide homogeneous information and more consistent features can be extracted based on image edges, an edge consistency radiation-change insensitive feature transform (EC-RIFT) method is proposed in this paper. Firstly, the noise and texture interference are reduced by preprocessing according to the image characteristics. Secondly, image edges are extracted based on phase congruency, and an orthogonal Log-Gabor filter is performed to replace the global algorithm. Finally, the descriptors are built with logarithmic partition of the feature point neighborhood, which improves the robustness of descriptors. Comparative experiments on datasets containing multi-source remote sensing image pairs show that the proposed EC-RIFT method outperforms other registration methods in terms of precision and effectiveness.