We present a novel complex-valued convolutional and multi-feature fusion network (CVCMFF Net) specifically for building semantic segmentation of InSAR images. It can effectively segment the layover, shadow, and background on both the simulated InSAR building images and the real airborne InSAR images. The segmentation performance of CVCMFF Net is significantly improved compared with other state-of-the-art networks. The comparative experiments are link to https://github.com/Jiankun-chen/building-semantic-segmentation-of-InSAR-images