The present invention provides a cell-specific replication-competent vector system, which does not target normal cells. The vector system is constructed by linking a transcriptional initiation regulatory promoter region upstream of a viral replication-related gene that integrates the linked region into a viral DNA vector. The constructed vector, when introduced into malignant tumor cells, selectively injures only tumor cells or proliferating smooth muscle cells of tumor neovascular tissue due to the selective expression of the regulatory promoter region upstream of a viral replication-related gene. In particular, the present invention relates to a transcriptional initiation regulatory region of the human calponin gene that can selectively express in tumor cells or proliferating smooth muscle cells of tumor neovascular tissue. The present invention also relates to methods of constructing the cell-specific replication-competent vector system and to treatment methods using the vector system by introducing the vector system into particular living tissues or cells such as malignant tumors and the like.