Disclosed is a method of synthesizing a (1R,2R)-nitroalcohol compound of formula (I), as shown in the following reaction scheme, including: subjecting a compound of formula (II) and a compound of formula (III) to a condensation reaction in an organic solvent in the presence of a copper complex generated in situ from a chiral (1S,2R)-amino alcohol ligand and a cupric salt to produce the (1R,2R)-nitroalcohol compound of formula (I), where R1 and R2 are defined in the same manner as that in the specification. The method involves mild reaction conditions, excellent diastereoselectivity and high chemical yield, and thus it is suitable for industrial applications.