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We investigate, on the basis of CCD Stroemgren photometry, the ages and metallicities of six LMC clusters together with their surrounding field population. The clusters and metallicities are: NGC 1651 (in the range [Fe/H]=-0.65dex to -0.41dex), NGC 1711 (-0.57±0.17dex), NGC 1806 (-0.71±0.23dex), NGC 2031 (-0.52±0.21dex) and NGC 2136/37 (-0.55±0.23dex) and NGC 2257 (-1.63±0.21dex). The metallicities for NGC 1651, NGC 1711, NGC 1806 and NGC 2031 have been determined for the first time (NGC 2031 and NGC 2136/37 are interesting for the Cepheid distance scale). In the cluster surroundings, we found about 650 field stars that were suitable to be used for a determination of an age-metallicity relation (AMR). Our method is to estimate ages for individual stars on the basis of Stroemgren isochrones with individually measured metallicities. With this method we are able to sample the AMR of the field population up to 8Gyr. Our metallicity data are incompatible with models predicting many metal-poor stars (G-dwarf problem). The metallicity of the field population increased by a factor of six, starting around 2Gyr ago. The proposed AMR is consistent with the AMR of the LMC cluster system (including ESO 121 SC03 and three clusters with an age of 4 Gyr). The proposed AMR is incompatible with the recently proposed AMR by Pagel & Tautvaisviene (1998MNRAS.299..535P).