A method for constructing a library containing single-stranded cyclic nucleic acids, comprising: randomly fragmenting a double-stranded nucleic acid sample with a transposase embedded complex, which comprises transposase and a first adaptor containing a transposase recognition sequence, to obtain fragmented double-stranded nucleic acids ligated with the first adaptor at each terminal thereof, with a gap between each 3'-end and the first adaptor; ligating with a ligase a second adaptor to the fragmented double-stranded nucleic acid at the gap after removing the transposase from the reaction system, the second adaptor having a sequence different from that of the first adaptor; performing a first PCR reaction with a pair of first primers each containing a uracil to obtain a first PCR product ligated with a first adaptor sequence and a second adaptor sequence respectively at two ends thereof; enzyme-digesting the first PCR product with User enzyme at the uracil site to generate a gap, followed by double-stranded cyclization resulting in double-stranded cyclic nucleic acids; subjecting the double-stranded cyclic nucleic acid, as a template, to constrained nick translation from the gap, where the amount of dNTPs is a critical restrictive factor for the constrained nick translation; removing a portion not affected by the constrained nick translation in the double-stranded cyclic nucleic acids by digestion to obtain double-stranded linear nucleic acids; ligating a third adaptor and an oligonucleotide adaptor sequence to the 3'-end and the 5'-end of each strand of the double-stranded linear nucleic acid, respectively; performing a second PCR reaction with a second primer containing a first affinity marker at the 5'-end thereof, to obtain a second PCR product ligated with a third adaptor sequence and the oligonucleotide adaptor sequence respectively at two ends thereof; capturing the second PCR product with a carrier having a second affinity marker capable of combining with the first affinity marker, and isolating single-stranded nucleic acids without the first affinity marker through nucleic acid denaturation; and cyclizing the single-stranded nucleic acids without the first affinity marker with a single-stranded cyclization "bridge" sequence which is capable of combining with the two ends of each single-stranded nucleic acid. randomly fragmenting a double-stranded nucleic acid sample with a transposase embedded complex, which comprises transposase and a first adaptor containing a transposase recognition sequence, to obtain fragmented double-stranded nucleic acids ligated with the first adaptor at each terminal thereof, with a gap between each 3'-end and the first adaptor; ligating with a ligase a second adaptor to the fragmented double-stranded nucleic acid at the gap after removing the transposase from the reaction system, the second adaptor having a sequence different from that of the first adaptor; performing a first PCR reaction with a pair of first primers each containing a uracil to obtain a first PCR product ligated with a first adaptor sequence and a second adaptor sequence respectively at two ends thereof; enzyme-digesting the first PCR product with User enzyme at the uracil site to generate a gap, followed by double-stranded cyclization resulting in double-stranded cyclic nucleic acids; subjecting the double-stranded cyclic nucleic acid, as a template, to constrained nick translation from the gap, where the amount of dNTPs is a critical restrictive factor for the constrained nick translation; removing a portion not affected by the constrained nick translation in the double-stranded cyclic nucleic acids by digestion to obtain double-stranded linear nucleic acids; ligating a third adaptor and an oligonucleotide adaptor sequence to the 3'-end and the 5'-end of each strand of the double-stranded linear nucleic acid, respectively; performing a second PCR reaction with a second primer containing a first affinity marker at the 5'-end thereof, to obtain a second PCR product ligated with a third adaptor sequence and the oligonucleotide adaptor sequence respectively at two ends thereof; capturing the second PCR product with a carrier having a second affinity marker capable of combining with the first affinity marker, and isolating single-stranded nucleic acids without the first affinity marker through nucleic acid denaturation; and cyclizing the single-stranded nucleic acids without the first affinity marker with a single-stranded cyclization "bridge" sequence which is capable of combining with the two ends of each single-stranded nucleic acid.