A 60 kV neutral Li beam is injected into the edge plasma of JET to measure the electron density. The beam observation system has been improved by replacing a Czerny-Turner spectrometer with a high-resolution transmission-grating spectrometer and a fast back-illuminated frame-transfer camera. The larger throughput of the spectrometer, the increased sensitivity, and the faster readout of the new camera allow inter-ELM (edge localized mode) measurements (frame rate of 100 Hz). The calibration of the setup, as well as an improved spectral fitting technique in the presence of carbon background radiation, is discussed in detail. The density calculation is based on a statistical analysis method. Results are presented for different plasma scenarios.