New measurements of the amount-of-substance density of pure CH4 in the temperature range 322 K to 700 K at pressures from 5 MPa to 35 MPa are reported. The results have been obtained by using a fully automated isochoric instrument and their uncertainty is estimated to be about +/-0.05 per cent at the lowest temperatures, rising to +/-0.1 per cent at the highest temperatures. Comparisons with the predictions of the recent empirical equation of state of Setzmann and Wagner, as well as with earlier experimental results, which the present work complements, are included.