The invention discloses copolyester and a preparation method and application thereof. The copolyester comprises binary acid components and binary alcohol components, wherein in the binary acid components, the content of the terephthalic acid structural unit is more than 90mol%; and in the binary alcohol components, the content of the ethylene glycol structural unit is 70-99mol%, and the content of the aliphatic dihydric alcohol structural unit which contains side chains and less than 6 carbon atoms is 1-30mol%. The copolyester also comprises a polyethylene glycol structural unit. Because the aliphatic dihydric alcohol structural unit which contains side chains and less than 6 carbon atoms and the polyethylene glycol structural unit are added to the copolyester, the copolyester can be made into fiber with the known method, and the fiber can be made into fabric. The prepared finished product has good dyeing property on disperse dye at normal temperature and pressure, thus the high equipment investment and operation cost resulted from high-temperature and high-pressure dying can be reduced.