In this paper, we propose an RTP/UDP/IP header compression method, Multiple-Reference Compression (MRC), which is designed for mobile multimedia communications. MRC is a compression method that calculates differences from the multiple reference headers that have already been sent and inserts them into a compressed header. The receiver can decompress the compressed header as long as at least one of the reference headers is correctly received and decompressed. MRC improves robustness against packet losses compared with CRTP defined in IETF RFC2508, and imposes less overheads and computational burden than robust header compression (ROHC) defined in RFC3095. We also implemented MRC and other header compression algorithms into our mobile testbed, and conducted multimedia streaming experiments over the testbed. The results of the experiments show that MRC offers the same level of packet loss rate as Legacy RTP for both audio and video streams, and provides better media quality than Legacy RTP and CRTP on error-prone radio links. Header compression robust against packet losses is expected as a key technology for VoIP and multimedia streaming services over 3G and future mobile networks.