Polycrystalline samples of Mn1-xCuxWO4 (x <= 0.5) have been prepared by a solid-state synthesis as well as from a citrate synthesis at moderate temperature (850 degrees C). The goal is to study changes in the structural, magnetic, and dielectric properties of magnetoelectric type-II multiferroic MnWO4 caused by replacing Jahn Teller-inactive Mn2+ (d(5), S = 5/2) ions with Jahn Teller-active Cu2+ (d(9), S = 1/2) ions. Combination of techniques including scanning electron microscopy, powder X-ray and neutron diffraction, and Raman spectroscopy demonstrates that the polycrystalline samples with low copper content 0 <= x <= 0.25 are solid solution that forms in the monoclinic P2/c space group. Rietveld analyses indicate that Cu atoms substitutes for Mn atoms at the Mn crystallographic site of the MnWO4 structure and suggest random distributions of Jahn Teller-distorted CuO6 octahedra in the solid solution. Magnetic susceptibility reveals that only 5% of Cu substitution suppresses the nonpolar collinear AF1 antiferromagnetic structure observed in pure MnWO4. Type-II multiferroicity survives a weak Cu substitution rate (x < 0.15). Multiferroic transition temperature and Neel temperature increase as the amount of Cu increases. New trends in some of the magnetic properties and in dielectric behaviors are observed for x = 0.20 and 0.25. Careful analysis of the magnetic susceptibility reveals that the incorporation of Cu into MnWO4 strengthens the overall antiferromagnetic interaction and reduces the magnetic frustration.