The ultrafine composite fibers consisting of lauric acid (LA) and polyamide 6 (PA6) as form-stable phase change materials (PCMs), were prepared successfully by electrospinning. The effect of carbon nanotubes (CNTs) on the structural morphology, phase change behaviors, thermal stability, flammability and thermal conductivity properties of electrospun LA/PA6 composite fibers was investigated by field-emission scanning electron microscopy (FE-SEM), differential scanning calorimetry (DSC), thermogravimetric analyses (TGA), microscale combustion calorimeter (MCC) and melting/freezing times measurements, respectively. SEM observations indicated that the LA/PA6 and LA/PA6/CNTs composite fibers possessed flat and ribbon-shaped morphologies, but the neat PA6 fibers had cylindrical shape with smooth surface; and the average fiber diameters for LA/PA6 composite fibers decreased generally with the addition of CNTs. DSC measurements indicated that the heat enthalpies of the composite fibers were lower that that of neat LA powders, while the amounts of CNTs had no appreciable effect on the phase change temperatures and heat enthalpies of the composite fibers. TGA results showed that the addition of CNTs increased the onset thermal degradation temperature, maximum weight loss temperature and charred residue at $700^{circ}C$ of the composite fibers, attributed to the improved thermal stability properties. It could be found from MCC tests that there were two-step combustion processes for composite fibers, and corresponded respectively to combustion of LA and polymer chains (PA6) in composite fibers. The addition of CNTs reduced the peak of heat release rate (PHRR) of electrospun composite fibers, contributing to the decreased flammability properties. The improved thermal conductivity performances of LA/PA6/CNTs composite fibers was also confirmed by comparing the melting/freezing times of LA/PA6 composite fibers with that of neat LA powders. The results from the SEM observation showed that the composite fibers had no appreciable variations in shape and diameter after heating/cooling processes.