Positions with subarcsecond accuracy have been measured for seven 22-GHz H2O masers associated with H II regions in the Large Magellanic Cloud (LMC); two of the masers are new detections. Initial position measurements were obtained with the 70-m antenna of the Canberra NASA Deep Space Network during a period of more than two years in which the antenna was used to monitor the maser emission. The positions were further improved using 22-GHz observations involving three antennas of the Australia Telescope Compact Array. The positions have been compared with those of 1.6-GHz continuum emission and other LMC masers (of OH and CH3OH). The H2O maser positions range from within 1 arcsec (270 mpc) of the centre of a compact H II component to beyond the boundary of significant continuum emission. Three of the four masers located near continuum peaks are close to OH masers. In two cases the positional agreement is better than 0.2 arcsec (53 mpc); in the third case the agreement is worse (0.9 arcsec) but the positions of the individual H2O features appear to be spread over more than 1 arcsec. The velocities of the OH masers are within the spread of the H2O velocities. The three H2O masers offset from continuum centres are located 3-7 arcsec from optical or infrared phenomena probably associated with very early stages of star formation; no other molecular masers are known in these directions.