Traditional polyurethane fibers (CPUF) are widely used in the preparation of blend clothing in order to improve the elasticity and comfort of fabrics. However, there has been a problem of low acid dye adsorption for CPUF, resulting in light hue of dyed CPUF. In this work, a poly (HMDI-BHOPA) was prepared with dicyclohexylmethane 4,4′-diisocyanate (HMDI) and 1,4-(2-hydroxyethyl) piperazine (BHOPA), and then added into the CPUF spinning solution for the preparation of modified polyurethane fibers (BPUFs) through dry-spinning technology. Tertiary amine groups were introduced after the addition of poly (HMDI-BHOPA), which could be protonated at acidic conditions to form binding sites for acid dyes, further enhancing the adsorption capacity of the fibers. Nuclear magnetic resonance spectroscopy (1H and 13C NMR) was used to confirm the structure of poly (HMDI-BHOPA). The results of differential scanning calorimetry (DSC) and thermogravimetry analysis (TGA) demonstrated that the addition of poly (HMDI-BHOPA) had little effect on the glass transition temperature and thermal stability of BPUFs. The addition of poly (HMDI-BHOPA) affected the ordered arrangement of hard segments and reduced crystallization enthalpy of hard and soft segments in polyurethane. Hence, the elastic recovery of BPUFs showed little change, and the elongation at break and break strength decreased compared to CPUF. Zeta potential testing results showed that BPUFs was protonated under acidic conditions. Dyeing results proved the enhancement of dyeability of BPUFs. The dyeing kinetics and thermodynamics of acid dyes on BPUFs were studied to investigate the dyeing mechanism. From the dyeing kinetics results, both CPUF and BPUFs fitted Elovich model. From dyeing thermodynamics results, Langmuir model showed a better applicability for BPUFs at a low pH and temperature condition, while Freundlich model fitted better for CPUF.