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Abstract We report the first results of a high-redshift (z≳ 5) quasar survey using the Dark Energy Spectroscopic Instrument (DESI). As a DESI secondary target program, this survey is designed to carry out a systematic search and investigation of quasars at 4.8 <z< 6.8. The target selection is based on the DESI Legacy Imaging Surveys (the Legacy Surveys) DR9 photometry, combined with the Pan-STARRS1 data andJ-band photometry from public surveys. A first quasar sample has been constructed from the DESI Survey Validation 3 (SV3) and first-year observations until 2022 May. This sample includes more than 400 new quasars at redshift 4.7 ≤z< 6.6, down to 21.5 magnitude (AB) in thezband, discovered from 35% of the entire target sample. Remarkably, there are 220 new quasars identified atz≥ 5, more than one-third of existing quasars previously published at this redshift. The observations so far result in an average success rate of 23% atz> 4.7. The current spectral data set has already allowed analysis of interesting individual objects (e.g., quasars with damped Lyαabsorbers and broad absorption line features), and statistical analysis will follow the survey’s completion. A set of science projects will be carried out leveraging this program, including quasar luminosity function, quasar clustering, intergalactic medium, quasar spectral properties, intervening absorbers, and properties of early supermassive black holes. Additionally, a sample of 38 new quasars atz∼ 3.8–5.7 discovered from a pilot survey in the DESI SV1 is also published in this paper.