Context. The Stellar Observation Network Group (SONG) is an initiative to build a worldwide network of 1m telescopes with high-precision radial-velocity spectrographs. Here we analyse the first radial-velocity time series of a red-giant star measured by the SONG telescope at Tenerife. The asteroseismic results demonstrate a major increase in the achievable precision of the parameters for red-giant stars obtainable from ground-based observations. Reliable tests of the validity of these results are needed, however, before the accuracy of the parameters can be trusted. Aims: We analyse the first SONG time series for the star 46 LMi, which has a precise parallax and an angular diameter measured from interferometry, and therefore a good determination of the stellar radius. We use asteroseismic scaling relations to obtain an accurate mass, and modelling to determine the age. Methods: A 55-day time series of high-resolution, high S/N spectra were obtained with the first SONG telescope. We derive the asteroseismic parameters by analysing the power spectrum. To give a best guess on the large separation of modes in the power spectrum, we have applied a new method which uses the scaling of Kepler red-giant stars to 46 LMi. Results: Several methods have been applied: classical estimates, seismic methods using the observed time series, and model calculations to derive the fundamental parameters of 46 LMi. Parameters determined using the different methods are consistent within the uncertainties. We find the following values for the mass M (scaling), radius R (classical), age (modelling), and surface gravity (combining mass and radius): M = 1.09 ± 0.04M⊙, R = 7.95 ± 0.11R⊙ age t = 8.2 ± 1.9 Gy, and logg = 2.674 ± 0.013. Conclusions: The exciting possibilities for ground-based asteroseismology of solar-like oscillations with a fully robotic network have been illustrated with the results obtained from just a single site of the SONG network. The window function is still a severe problem which will be solved when there are more nodes in the network. Based on observations made with the Hertzsprung SONG telescope operated at the Spanish Observatorio del Teide on the island of Tenerife by the Aarhus and Copenhagen Universities and by the Instituto de Astrofísica de Canarias.