Provided is a method of isolating and purifying nucleic acids using an immobilized hydrogel or polyethylene glycol (PEG)-hydrogel copolymer. The method includes: immobilizing a functional group-containing hydrogel or PEG-hydrogel copolymer on a substrate; adding a mixed sample solution containing a salt and nucleic acids to the hydrogel- or PEG-hydrogel copolymer-immobilized substrate to bind the nucleic acids to the hydrogel or the PEG-hydrogel copolymer; washing the nucleic acid-bound hydrogel or PEG-hydrogel copolymer; and eluting the nucleic acids from the hydrogel or the PEG-hydrogel copolymer using an elution solvent. Therefore, binding and elution of nucleic acids can be performed even with no addition of a separate chemical substance, and an effect on a subsequent process such as PCR can be minimized. Furthermore, the amount and intensity for binding nucleic acids can be adjusted according to PEG concentration, and the presence of a hydrogel compound on a substrate enables patterning.