Flexible shape-stabilized composite phase change materials (ss-CPCMs) have a wide range of potential applications because they can be woven into desired shapes. In this work, a series of novel flexible paraffin/multi-walled carbon nanotubes (MWCNTs)/polypropylene hollow fiber membrane (PHFM) ssCPCMs (PC-PHFM-CPCMs) with weavability were fabricated for thermal energy storage. In order to select a PHFM with optimum stretching ratio as the supporting material for the flexible ss-CPCMs, PHFMs with different stretching ratios were fabricated to encapsulate the paraffin as novel flexible ss-CPCMs (PPHFM-CPCMs). The effects of stretching ratios on the latent heats and absorption capacity were investigated. PHFM200 (polypropylene hollow fiber stretched by 200%) showed the high porosity (65.2%) and tensile strength (119.9 MPa), and the corresponding P-PHFM-CPCM200 had the largest latent heats in the melting process and solidifying process (73.90 and 76.71 J/g) and maximum paraffin absorption capacity (52.42 wt%) compared to other candidates. Paraffin /MWCNTs mixtures with high thermal conductivity were injected into the columned cavity of P-PHFM-CPCM200 to further enhance the paraffin encapsulation capacity and significantly improve their heat transfer. Among all PC-PHFM-CPCMs, PCO-PHFM-CPCM200 exhibited the maximum paraffin encapsulation capacity of 80.97 wt%. The thermal conductivity of PC-PHFM-CPCMs was obviously enhanced with the increase in the weight ratio of MWCNTs. PC4-PHFM-CPCM200 achieved the highest thermal conductivity of 0.46 W/m K, which was obviously improved by 100%. The corresponding latent heat in the solidification process was 109.2 J/g. In addition, excellent chemical compatibility and thermal stability of PC-PHFM-CPCMs were demonstrated by the Fourier transform infrared spectroscopy and thermogravimetric analysis.