We present radio observations of the black hole X-ray transient XTE J1720−318, which was discovered in 2003 January as it entered an outburst. We analyse the radio data in the context of the X-ray outburst and the broad-band spectrum. An unresolved radio source was detected during the rising phase, reaching a peak of nearly 5 mJy approximately coincident with the peak of the X-ray light curve. A study of the spectral indices suggests that at least two ejection events took place, with the radio-emitting material expanding and becoming optically thin as it faded. The broad-band spectra suggested that the accretion disc dominated the emission, as expected for a source in a soft state. The radio emission decayed to below the sensitivity of the telescopes for 6 weeks but switched on again during the transition of the X-ray source to the low/hard state. At least one 'glitch' was superimposed on the otherwise exponential decay of the X-ray light curve, which was reminiscent of the multiple jet ejections of XTE J1859+226. We also present a Ks-band image of XTE J1720−318 and its surrounding field taken with the Very Large Telescope.