A temperature and humidity sensor based on cascaded fiber Bragg gratings comprising tapered coreless fibers is designed. A composite nanofiber membrane is prepared for this sensor comprising a layer of polyvinyl alcohol/carboxymethyl cellulose nanofibers, each containing a biconical connector prepared by electrospinning in the cone area. Changes in humidity change the effective refractive index and thickness of the nanofiber film, thereby affecting the transmission loss of light through the fiber, and then changing the output spectral power. In addition, temperature fluctuations cause the center wavelength of the fiber grating to shift. Monitoring the peak power and peak wavelength of the output spectrum (changes in the center wavelength) enables temperature and humidity sensing. Temperature and humidity response tests are performed on the designed sensor. The relative humidity sensitivity of the sensor is 0.0198 dB/%, and the relative temperature sensitivity is 11.730 pm/℃. Results show that electrospinning is an effective method for preparing moisture-sensitive coatings on the surface of optical fiber sensors.