We have constructed a magneto-optical trap (MOT) for metastable triplet helium atoms utilizing the 2 3S1 -> 3 3P2 line at 389 nm as the trapping and cooling transition. The far-red-detuned MOT (detuning Delta = -41 MHz) typically contains few times 10^7 atoms at a relatively high (~10^9 cm^-3) density, which is a consequence of the large momentum transfer per photon at 389 nm and a small two-body loss rate coefficient (2 * 10^-10 cm^3/s < beta < 1.0 * 10^-9 cm^3/s). The two-body loss rate is more than five times smaller than in a MOT on the commonly used 2 3S1 -> 2 3P2 line at 1083 nm. Furthermore, we measure a temperature of 0.46(1) mK, a factor 2.5 lower as compared to the 1083 nm case. Decreasing the detuning to Delta= -9 MHz results in a cloud temperature as low as 0.25(1) mK, at small number of trapped atoms. The 389 nm MOT exhibits small losses due to two-photon ionization, which have been investigated as well.