A method and reagent for constructing a nucleic acid double-linker single-strand cyclic library. The method comprises: breaking a nucleic acid into nucleic acid fragments; connecting a first linker sequence; producing by amplification a first product provided with the first linker sequence at either end, where a U nucleobase site is provided on primer sequences and a nicking enzyme recognition sequence is either provided or not provided on same, and a first affinity tag is provided on one of the primer sequences; using USER enzyme to cleave the first product; cyclizing the cleaved first product; treating the cyclization product with either a phosphatase or a nicking enzyme; using a solid-phase vector for combination with a cyclized molecule; performing a restrictive gap translation reaction; removing by digestion any portion that did not undergo the restrictive gap translation reaction; connecting a second linker sequence; producing by amplification a second product provided with the second linker sequence at either end; denaturing the second product, and cyclizing a single-strand nucleic acid molecule. The method allows an increase in the length of library insert fragments, a simplified library construction process, reduced library construction time, and reduced library construction costs.