This study focuses on exploiting the dynamic social multimedia behaviors to infer the stable demographic attributes. Existing demographic attribute inference studies are devoted to developing advanced features/models or exploiting external information and knowledge. The conflicts between dynamicity of behaviors and the steadiness of demographic attributes are largely ignored. To address this issue, we introduce a cross-OSN approach to discover the shared stable patterns from users' social multimedia behaviors on multiple Online Social Networks (OSNs). The basic assumption for the proposed approach is that, the same user's cross-OSN behaviors are the reflection of his/her demographic attributes in different scenarios. Based on this, a coupled projection matrix extraction method is proposed for solution, where the cross-OSN behaviors are collectively projected onto the same space for demographic attribute inference. Experimental evaluation is conducted on a self-collected Google+ and Twitter dataset consisting of four types of demographic attributes as gender, age, relationship and occupation. The experimental results demonstrate the effectiveness of cross-OSN based demographic attribute inference.