Increasing trends of natural organic matter (NOM) in surface water in Nordic countries may cause future problems for drinking water producers. Emerging membrane technology, such as ultrafiltration (UF) and nanofiltration (NF), has the potential to produce safe drinking water of good quality from sources with high organic concentrations. In the present pilot study, surface water from three sources was treated by direct filtration on a hollow fiber ultrafilter (HFUF) and/or a hollow fiber nanofilter (HFNF). UV-absorbance (UVA) and total organic carbon (TOC) showed a high percentage of NOM removal by HFUF/coagulation, with retentions of around 75% for UVA and 55% for the TOC. NOM removal was notably greater by HFNF; with 93% in UVA retention and 88% in TOC retention. Regrettably, the water treated with HFNF retained 20–35% of the desired hardness. HFUF achieved retention comparable to traditional flocculation and sedimentation steps, while HFNF achieved even better removal of NOM. Importantly, results indicate that a membrane process with only an additional polishing step would result in decreased concentrations of NOM in the drinking water, even with higher organic loads in the raw water.