Recently, SCTP is attracting attention to support mobility in the Internet because it does not require additional equipment such as the Home Agent of Mobile IP. This paper focuses on an SCTP fast handover mechanism using a single interface because it is assumed that small mobile devices have a single interface per communication medium such as IEEE802.11b due to hardware limitations. The proposed mechanism called SCTPmx employs a cross layer control information exchange system called LIESto predict handover. LIES was originally designed to achieve network layer fast handover and then it was extended by adding the network layer primitives for efficient interaction among the link layer, the network layer, and the transport layer. Prior to handover, SCTPmx can generate a new address that will be used after handover and can execute duplicate address detection of IPv6. SCTPmx can suppress the delay caused by channel scanning at the link layer by employing selective background scanning mechanism which allows to continue data communication during channel scanning. In addition, SCTPmx can notify the correspondent node of the new address before handover. SCTPmx was implemented on FreeBSD. SCTPmx achieved better than 25 times lower handover latency (100msec) and 2 times higher throughput than previous proposals.