A one-step spun composite DTY and preparation method thereof are provided. The bi-profiled fiber is manufactured with two types of modified polyester of different viscosities through the steps of melting, melt metering, composite extruding, cooling, oiling, drawing, heat setting and winding. Wherein those two modified polyesters have a molecular structure including terephthalic acid segments, ethylene glycol segments and branched diol segments, and the branched diol has a structural formula of here R1 and R2 are separately selected from the linear alkylene with 1-3 carbon atoms, R3 from the alkyl with 1-5 carbon atoms, and R4 from the alkyl with 2-5 carbon atoms. The obtained one-step spun composite DTY has an elastic shrinkage rate of no less than 35%. The method presented in this invention is involved in a simple and reasonable technological process for wide application range.