The invention discloses a synthesis method of tasimelteon. The synthesis method comprises steps as follows: a compound (I) is subjected to an epoxidation reaction, and a compound (II) is obtained; the compound (II) and diethyl cyanomethylphosphonate are subjected to a ring-closure reaction under the protection of inert gas, and a compound (III) is obtained; the compound (III) is subjected to a reduction reaction, and a compound (IV) is obtained; the compound (IV) is subjected to an acylation reaction, and tasimelteon (V) is obtained. The route is simple, 4-vinyl dihydrobenzofuran is taken as a raw material and subjected to four steps of reactions including epoxidation, cyclopropanation, reduction and acylation, and the target product tasimelteon (V) is prepared. The reaction efficiency is greatly improved, the reaction steps are reduced, the operation procedures are simplified, and a new approach for synthesis of tasimelteon is provided. Besides, the method is suitable for industrial production and has great practical application value and social and economic benefits.