1. (I) A method for producing a protein of interest, comprising introducing a protein expression vector which comprises a gene fragment comprising a DNA encoding a protein of interest and a selectable marker gene transposon sequences at both terminals of the gene fragment, into a suspension mammalian cell; the integrating the gene fragment inserted between a pair of the transposon sequences, into a chromosome of the mammalian cell to obtain a mammalian cell capable of expressing a protein of interest; and suspension-culturing the mammalian cell; (II) a method for producing a protein of interest, which comprises the following steps (A) to (C): (A) a step of simultaneously introducing the following expression vectors (a) and (b) into a suspension mammalian cell (a) an expression vector which comprises a gene fragment comprising a DNA encoding a protein of interest and transposon sequences at both terminals of the gene fragment, (b) an expression vector which comprises a DNA encoding a transposase which recognizes the transposon sequences and has activity of transferring a gene fragment inserted between a pair of the transposon sequences into a chromosome, (B) a step of transiently expressing the transposase transiently from the expression vector introduced in the step (A) to integrate the gene fragment inserted between a pair of the transposon sequences into a chromosome of the mammalian cell to obtain a suspension mammalian cell capable of expressing the protein of interest, and (C) a step of suspension-culturing the suspension mammalian cell capable of expressing the protein of interest obtained in the step (B) to produce the protein of interest. (III) a method for obtaining a suspension mammalian cell capable of expressing a protein of interest, comprising introducing a protein expression vector which comprises a gene fragment comprising a DNA encoding a protein of interest and a selectable marker gene and transposon sequences at both terminals of the gene fragment into a suspension mammalian cell; and integrating the gene fragment inserted between a pair of the transposon sequences, into a chromosome of the mammalian cell.