A piezoresistive flexible strain sensor was developed using thermoplastic polyurethane elastomers (TPU) as the matrix and carbon nanotubes (CNTs) as conductive fillers. Sensitivity, strain range, and tensile cycling stability were concurrently considered during its design. Electrospun TPU fiber membranes were prepared via electrospinning in this experiment, with controllable fiber diameter achieved by adjusting the rotational speed of the electrospinning receiving drum. CNTs were incorporated into a flexible polymer substrate through suction filtration to create the strain sensor. The support structure of the electrospun film served as a carrier for uniformly adhering conductive particles. Well-dispersed conductive CNTs could more easily achieve uniform loading through the pore size of the electrospun fiber film, thereby forming a conductive layer. This study initially determined the influence of TPU content in the spinning solution on the morphology of the electrospun membrane. Subsequently, the effects of CNT content and electrospinning receiving drum rotational speed on the microstructure of TPU electrospun membranes were investigated, along with their impact on the microstructure, mechanical properties, and sensing performance of CNTs/TPU (CT) flexible strain sensors. The results indicate that the electrospun fiber membrane prepared under the conditions of TPU mass fraction of 20 wt% and rotational speed of 100 r/min has a larger average fiber diameter and a more stable scaffold structure. The CNTs/TPU (CT) sensor, prepared by filtering 10 mL of CNTs with a concentration of 2 mg/mL, exhibited the best mechanical properties, with a tensile strength and elongation at break of 6.22 MPa and 575 %, respectively. Additionally, it demonstrated high sensitivity (GF = 420.17 at 200 % strain) and excellent durability stability (300 cycle tests), enabling quick and accurate responses to movements of various parts of the human body, thereby meeting the basic usage requirements of flexible strain sensors.