A method for constructing a library of single-stranded cyclic nucleic acid fragments having double adaptors, comprising the following steps: disrupting a nucleic acid into nucleic acid fragments for library construction; ligating a first adaptor sequence to both ends of the nucleic acid fragments; performing a first PCR amplification to obtain first products having the first adaptor sequence at both ends, wherein the primer sequences used in the first PCR have a uracil base site; digesting the first products with a USER enzyme to form sticky ends, followed by cyclization to generate a gap; or alternatively, in the case that the primer sequences used in the first PCR also have a nickase recognition sequence, digesting the first products with a USER enzyme to form sticky ends, followed by cyclization, and then followed by digestion of the cyclized products with a nickase to generate a nick; initiating controlled nick/gap translation reaction from the nick or gap by using the cyclic nucleic acid molecules as template, wherein the controlled nick/gap translation can move the gaps or nicks around the cyclic nucleic acid molecules, such that the gaps or nicks are located in the nucleic acid fragment and the length of the fragment can be controlled; digesting and removing the portion of the respective cyclic nucleic acid molecules that does not undergo the controlled nick/gap translation reaction to obtain linear nucleic acid molecules, which comprises: first digesting the cyclic nucleic acid molecules with an enzyme having 5'-3' exonuclease activity until the gaps at both ends meet; and then digesting the resulting single strands with an enzyme having 3'-5' exonuclease activity or a single strand exonuclease; ligating a second adaptor sequence to both ends of the linear nucleic acid molecules; performing a second PCR amplification to obtain second products having the second adaptor sequence at both ends; and denaturing the second products to obtain single-stranded nucleic acid molecules, and cyclizing one of the single-stranded nucleic acid molecules with a mediating sequence complementary to both ends of the single-stranded nucleic acid molecule to obtain the library of single-stranded cyclic nucleic acid fragments having double adaptors. disrupting a nucleic acid into nucleic acid fragments for library construction; ligating a first adaptor sequence to both ends of the nucleic acid fragments; performing a first PCR amplification to obtain first products having the first adaptor sequence at both ends, wherein the primer sequences used in the first PCR have a uracil base site; digesting the first products with a USER enzyme to form sticky ends, followed by cyclization to generate a gap; or alternatively, in the case that the primer sequences used in the first PCR also have a nickase recognition sequence, digesting the first products with a USER enzyme to form sticky ends, followed by cyclization, and then followed by digestion of the cyclized products with a nickase to generate a nick; initiating controlled nick/gap translation reaction from the nick or gap by using the cyclic nucleic acid molecules as template, wherein the controlled nick/gap translation can move the gaps or nicks around the cyclic nucleic acid molecules, such that the gaps or nicks are located in the nucleic acid fragment and the length of the fragment can be controlled; digesting and removing the portion of the respective cyclic nucleic acid molecules that does not undergo the controlled nick/gap translation reaction to obtain linear nucleic acid molecules, which comprises: first digesting the cyclic nucleic acid molecules with an enzyme having 5'-3' exonuclease activity until the gaps at both ends meet; and then digesting the resulting single strands with an enzyme having 3'-5' exonuclease activity or a single strand exonuclease; ligating a second adaptor sequence to both ends of the linear nucleic acid molecules; performing a second PCR amplification to obtain second products having the second adaptor sequence at both ends; and denaturing the second products to obtain single-stranded nucleic acid molecules, and cyclizing one of the single-stranded nucleic acid molecules with a mediating sequence complementary to both ends of the single-stranded nucleic acid molecule to obtain the library of single-stranded cyclic nucleic acid fragments having double adaptors.