Wearable pressure sensors with high sensitivity, fast response time, and low detection limit have great potential for blood pressure monitoring and early diagnosis of hypertension. This article introduces a piezoresistive pressure sensor based on carbon nanotubes (CNTs), polyaniline (PAni), and fabric (CNT/PAni/fabric) for health monitoring applications. This sensor is made by using two layers of linen fabric coated with CNT and PAni. These layers are placed on a polyester fabric substrate. One of the coated layers has a mesh structure, which increases the sensitivity of the sensor and lowers its detection limit. The CNT/PAni/fabric sensor has a high sensitivity of 2.035 kPa−1 at pressures from 0 to 0.2 kPa, a response time of 290 ms, and a detection limit of 1.5 Pa. These features make it suitable for measuring blood pressure. The results obtained by measuring blood pressure using the pulse transit time method on four people, compared with the values obtained using the digital sphygmomanometer, show a discrepancy ranging between 0.019% and 1.62%. Also, the average error and standard deviation for the sensor measurement in systolic and diastolic pressures are 0.56 ± 0.33 and 0.57 ± 0.46, respectively, which shows that measurement with this sensor can be an alternative to existing devices.