Object is to provide a method of constructing a library of peptides having, at a desired position in the random sequence of each peptide, an amino acid having a portion capable of binding to a target. The invention provides a method of producing a library of peptides having, at a designated position in the random sequence of each peptide, a special amino acid having a portion capable of binding to a target, including (i) preparing a library of mRNAs having, in the mRNA sequence coding for a random amino acid sequence, a base sequence having an altered codon encoding the special amino acid, (ii) preparing an aminoacyl tRNA with the special amino acid linked to a tRNA encoded by the altered codon, and (iii) translating the mRNAs by using a cell-free translation system containing the aminoacyl tRNA to obtain a library of peptides having, in the random sequence thereof, a predetermined special amino acid.