Due to the low sampling rate of the camera based receiver, the movement of communication devices becomes a factor that cannot be ignored in the demodulation of optical camera communications (OCC). In this paper, we propose the block matching demodulation (BMD) algorithm, which is a movement-robust and optical-interference-resistant demodulation method for OCC. The BMD algorithm can resist the movement of communication devices by locating communication light source per image and immunize optical interference by utilizing the fast time-varying characteristic of communication light source. Moreover, in order to enhance the reliability of communication systems, BMD algorithm and Manchester decoding are combined to realize error detection and correction without increasing the overhead of encoding. Finally, we build a practical mobile OCC system to test the performance of BMD algorithm. Experimental results show that the BMD algorithm can resist the movement of communication devices effectively and achieve reliable demodulation.