Large volume zinc tungstate crystal scintillators (up to 50 mm in diameter and 100 mm length) with improved energy resolution were developed as a result of advances in crystal growth. The energy resolution of one-centimeter cube ZnWO4 crystals showed energy resolution in the range 8-10% for 662 keV gamma line of 137Cs. A value of 13.7% has been obtained with a large sample Oslash44 times 55 mm. The radioactive contamination of a ZnWO4 26 times 24 times 24 mm detector was tested in the Solotvina Underground Laboratory. The obtained results demonstrate ability to use ZnWO4 in order to search for 2beta-decay of zinc and tungsten.