We demonstrated the fabrication of a low-cost and high-resolution papercraft smartphone spectrometer and characterized its performance by recording spectra from gas discharge lamps. The optical design and a lab-made narrow slit used in the fabrication led to fine images of the slit on the image sensor, resulting in high spectral resolution. The spectral resolution of the fabricated papercraft smartphone spectrometer was measured to be 0.5 nm, which is similar to that of the best smartphone spectrometer reported thus far. Extending the exposure time of the phone's camera revealed the fine structure of a spectrum with high sensitivity. The build cost of the papercraft smartphone spectrometer was less than $3. We demonstrated that the papercraft smartphone spectrometer is a low-cost device that can record spectra with high resolution and high sensitivity.