A vector of the present invention is a vector for amplifying a target gene in a mammalian cell, the vector including an amplification-activating fragment, which is a partial fragment of a mammalian replication initiation region and has a gene amplification activity site, and a mammalian nuclear matrix attachment region. In the case where the mammalian replication initiation region as described above derives from a c-myc locus, for example, the above-described partial fragment at least contains a duplex unwinding element and a topoisomerase II-binding domain. The vector as described above improves gene transfer efficiency and gene amplification efficiency compared with the existing high gene amplification systems. Thus, a method whereby a “high gene amplification system” developed by the inventors can amplify a target gene with better gene transfer efficiency and a vector to be used in this method are provided.