The fatty acid ternary eutectics such as capric-lauric-myristic acid, capric-lauric-palmitic acid, capric-lauric-stearic acid, capric-myristic-palmitic acid, capric-myristic-stearic acid, and capric-palmitic-stearic acid and quaternary eutectics such as capric-lauric-myristic-palmitic acid, capric-lauric-myristic-stearic acid, capric-lauric-palmitic-stearic acid, capric-myristic-palmitic-stearic acid, and lauric-myristic-palmitic-stearic acid were selected as solid-liquid phase-change materials (PCMs). And then the innovative ternary eutectic/polystyrene (PS)/ternary eutectic and ternary eutectic/PS/quaternary eutectic form-stable phase-change composite fibrous membranes (PCCFMs) were directly prepared by the co-electrospinning method under the same spinning parameters. The as-prepared form-stable PCCFMs exhibited three-dimensional fibrous network structure with the average fiber diameter of about 410–780 nm according to the scanning electron microscopy images. The adhesion among nanofiber intersections was observed occasionally. The differential scanning calorimetry results showed that fatty acid eutectics have been successfully combined into the form-stable PCCFMs, and their melting peak temperatures mostly ranged from 15°C to 21°C with a temperature interval of 1°C. Moreover, the phase-change enthalpies reached about 40–61 kJ kg−1. It is concluded that these electrospun form-stable PCCFMs with appropriate phase-change temperatures could be considered as potential PCMs to be applied in thermo-regulating fibers and textiles.