A novel cosmid vector and the like effectively used in generating a recombinant adenoviral vector are provided. More specifically, there are provided a cosmid vector characterized by: (1) containing an adenoviral genome having adenoviral inverted terminal repeat sequences each having a complete nucleotide sequence, (2) having a deletion in an adenovirus E1 gene region, and (3) containing a restriction enzyme recognition sequence not present in the adenoviral genome, on both sides of the adenoviral genome; a method of generating a recombinant adenoviral vector using the cosmid vector; and a reagent for generating a recombinant adenoviral vector containing the cosmid vector as a component.