To improve the elastic recovery of common poly(ester-ether) fibers, especially under lower temperatures, an imide dicarboxylic acid was prepared with trimellitic anhydride and aminobenzoic acid firstly, and then series of poly(ester-ether-imide) block copolymer(CPI) were prepared with this imide dicarboxylic acid, terephthalic acid, 1,4-butanediol and polytetrahydrofuran glycol .etc. The stuctures and properties were investigated by FT-IR spectra, differential scanning calorimetry(DSC) and capillary Ubbelohde. It was found that the Tm of the polymer was about 140°C and the intrinsic viscosity was 0.7~0.9dL/g. The CPI copolymers were melting spinning. The draw ratio and test temperature effects to the fibers' elastic recovery were studied. The results showed that stretching is beneficial to the improvement of the elastic recovery; the modified fibers' delayed elastic recovery was above 92% at 28°C and over 95% at lower temperatures of 5°C and -10°C, which is a great improvement to the common poly(ester-ether) fibers'.